Rear window defogger connector not working 2006 yukon" broke off window

System Description NEEL0216 MODELS WITHOUT POWER DOOR LOCKS NEEL0216S01 The rear window defogger system is controlled by the rear window defogger timer. The rear window defogger operates only for approximately 15 minutes. The rear window defogger switch is integral to the air control. Power is supplied at all times
to rear window defogger relay terminal 5
through 20A fuse [No. 25, located in the fuse block (J/B)]. With the ignition switch in the ON or START position, power is supplied
through 10A fuse [No. 5, located in the fuse block (J/B)]
to rear window defogger relay terminal 1, and
to rear window defogger timer terminal 1. Ground is supplied to air control (rear window defogger switch) terminal 8 and rear window defogger timer terminal 4 through body grounds M14 and M68. With the rear window defogger switch (located in air control) ON, ground is supplied
to rear window defogger timer terminal 3
through air control (rear window defogger switch) terminal 8. Rear window defogger timer terminal 2 then supplies ground to the rear window defogger relay terminal 2. With power and ground supplied, the rear window defogger relay is energized. Power is supplied
through terminal 3 of the rear window defogger relay
to rear window defogger terminal +. Rear window defogger terminal - is grounded through body ground R102. With power and ground supplied, the rear window defogger filaments heat and defog the rear window. When the system is activated, the rear window defogger indicator illuminates in the air control. Power is supplied
from rear window defogger relay terminal 3
to air control (rear window defogger switch) terminal 4. Air control terminal 8 is grounded through body grounds M14 and M68. MODELS WITH POWER DOOR LOCKS NEEL0216S02 The rear window defogger system is controlled by the smart entrance control unit. The rear window defogger operates only for approximately 15 minutes. The rear window defogger switch is integral to the air control. Power is supplied at all times
to rear window defogger relay terminal 5
through 20A fuse [No. 25, located in the fuse block (J/B)] and
to smart entrance control unit terminal 49
through 7.5A fuse [No. 28, located in the fuse block (J/B)]. With the ignition switch in the ON or START position, power is supplied
through 10A fuse [No. 5, located in the fuse block (J/B)]
to rear window defogger relay terminal 1 and
to smart entrance control unit terminal 27. Ground is supplied to air control (rear window defogger switch) terminal 8 and smart entrance control unit terminals 43 and 64 through body grounds M14 and M68. With the rear window defogger switch (located in air control) ON, ground is supplied
to smart entrance control unit terminal 14
through air control (rear window defogger switch) terminal 1. Smart entrance control unit terminal 37 then supplies ground to the rear window defogger relay terminal 2. With power and ground supplied, the rear window defogger relay is energized. Power is supplied
through terminal 3 of the rear window defogger relay
to rear window defogger terminal +.
Rear window defogger terminal - is grounded through body ground R102. With power and ground supplied, the rear window defogger filaments heat and defog the rear window. When the system is activated, the rear window defogger indicator illuminates in the air control. Power is supplied
from rear window defogger relay terminal 3
to air control (rear window defogger switch) terminal 4. Air control (rear window defogger switch) terminal 8 is grounded through body grounds M14 and M68

Doesn't use a relay , controlled by lift gate control module . Your best bet , take it to a qualified repair shop .
Rear Window Defogger System Components
The rear window defogger system consist of the following components:
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HVAC control module

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Liftgate module (LGM)/endgate module (EGM)

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Rear window defogger grid

Rear Window Defogger Operation (With LGM)
Battery positive voltage is supplied through the LGM 2 fuse to the LGM for the rear window defogger system. When the rear window defogger switch is depressed, the HVAC control module illuminates the rear window defogger indicator, and sends a class 2 message to the LGM to enable the rear window defogger. The LGM enables the rear window defogger by allowing battery positive voltage to the rear window defogger.
When the rear window defogger switch is pressed for the first time, the defogger cycle lasts 10 minutes. Further operation results in 10 minute defogger cycles.
DTC B0283 Electric Rear Defrost Circuit - do you know what DTC'S - diagnostic trouble code's are ?
Circuit Description
The liftgate module (LGM)/endgate module (EGM) monitors the voltage level on the supply voltage circuit of the rear window defogger. The LGM/EGM test the supply voltage circuit of the rear window defogger every 160 milliseconds. With the rear window defogger inactive, the supply voltage circuit of the rear window defogger will have no voltage present. With the rear window defogger active, the supply voltage circuit of the rear window defogger will be near system voltage.

As by heat only works some of the time , you mean it doesn't blow air out of the vent's . This means you probably have a problem with the blower motor or blower motor resistor or blower motor relay .
Rear Window Defogger Inoperative

Exchange the rear defogger relay with a known good relay from the under hood junction block.
1. Turn the ignition switch to the ON position.
2. Press the rear defogger switch to the ON position.

Does the rear defogger grid warm?
--
Yes Go to Step 2
NO Go to Step 3

2

Replace the faulty relay.
Is the repair complete?
Go to Defogger System Check --

3

1. Use a fused jumper wire in order to backprobe between terminal A4 of underhood junction block connector C3 and ground.
2. Use a test lamp in order to backprobe between terminal C5 of underhood junction block connector C3 and ground.

Does the test lamp light?
--
Go to Step 4
Go to Step 23

4

1. Use a test lamp in order to backprobe between terminal C5 of underhood junction block connector C3 and ground.
2. Press the rear defogger switch to the ON position.

Does the test lamp light?
--
Go to Step 5
Go to Step 14

IF you checked the fuses and relays, them it sound like it might be wiring or wiring connector might be loose.

There is a module that controls the rear window defogger grid . LGM/ EGM Liftgate or endgate module .Receive's message on class 2 serial data network from the HVAC control module to turn it on when button pressed . Fuse # 3 30 amp located in the rear fuse box . Do you know where the rear fuse box is ?
Rear Window Defogger Description and Operation
Rear Window Defogger System Components
The rear window defogger system consist of the following components:
• HVAC control module
• Liftgate module (LGM)/endgate module (EGM)
• Rear window defogger grid
Rear Window Defogger Operation (With LGM)
Battery positive voltage is supplied through the LGM 2 fuse to the LGM for the rear window defogger system. When the rear window defogger switch is depressed, the HVAC control module illuminates the rear window defogger indicator, and sends a class 2 message to the LGM to enable the rear window defogger. The LGM enables the rear window defogger by allowing battery positive voltage to the rear window defogger.
When the rear window defogger switch is pressed for the first time, the defogger cycle lasts 10 minutes. Further operation results in 10 minute defogger cycles.
Rear Window Defogger Operation (With EGM)
Battery positive voltage is supplied through the EGM 2 fuse to the EGM for the rear window defogger system. When the rear window defogger switch is depressed, the HVAC control module illuminates the rear window defogger indicator, and sends a class 2 message to the EGM to enable the rear window defogger. The EGM enables the rear window defogger by allowing battery positive voltage to the rear window defogger.
The following conditions must be met for rear window defogger to operate:
• The end gate glass position is not below the index position.
• The window express down movement is not requested.
• The window down movement is not requested.
If the end-gate glass is not fully closed, the DIC displays "Tailgate Glass Down" when the rear defogger operation is attempted.
When the rear window defogger switch is pressed for the first time, the defogger cycle lasts 10 minutes. Further operation results in 10 minute defogger cycles.

Fuse Block - Rear
Beneath the left rear seat

Rear Defogger Inoperative, But Heated Mirrors Operate Correctly
1. Connect scan tool. Turn ignition switch to RUN position. Turn rear defogger on. Using scan tool, display BCM
outputs. If rear defogger is being requested on, go to next step. If rear defogger is not being requested on, go to
step 10).
2. Ensure ignition switch is in RUN position. Remove rear defogger relay from rear junction block, located on center
right rear of passenger compartment, under rear seat. Connect test light between ground and defogger relay
harness connector terminal F3 (Brown wire). If test light illuminates, go to next step. If test light does not
illuminate, go to step 11).
3. Connect test light between ground and defogger relay harness connector terminal A2 (Red wire). If test light
illuminates, go to next step. If test light does not illuminate, go to step 12).
4. Connect test light between defogger relay harness connector terminals A2 (Red wire) and B3 (Purple wire). If test
light illuminates, go to step 13). If light does not illuminate, go to next step.
5. Disconnect rear defogger positive and negative feed bus connectors. Connect a jumper wire between defogger
relay harness connector terminals F3 (Brown wire) and A4 (White wire). Connect test light between ground and
positive feed bus connector terminal "A" (Black wire). If test light illuminates, go to next step. If test light does not
illuminate, go to step 8).
6. Connect test light between positive feed bus connector terminal "A" (Black wire) and negative feed bus connector
terminal "B" (Black wire). If test light illuminates, go to next step. If test light does not illuminate, go to step 9).
7. Repair open in Black wire between rear defogger and ground. Recheck system operation.
8. Repair open in Purple wire between rear junction block and heated backlight antenna module. Recheck system
operation.
9. Check for proper terminal contact at rear defogger connectors. Repair as necessary. Recheck system operation.
10. Check for proper terminal contact at BCM. If terminal contact is okay, replace BCM. Recheck system operation.
11. Repair open in Brown wire between rear junction block and instrument panel junction block. Recheck system
operation.
12. Repair open in Red wire between rear junction block and underhood junction block (located in right front corner of
engine compartment, between battery and strut tower). Recheck system operation.
13. Connect test light between defogger relay harness connector terminals F3 (Brown wire) and A4 (White wire). If
test light illuminates, go to next step. If test light does not illuminate, go to step 16).
14. Reinstall defogger relay. Disconnect BCM 32-pin Pink connector C2. BCM is located behind right side of instrument
panel, near rear of glove box. Using DVOM, check voltage between ground and BCM harness connector C2
terminal A3 (White wire). If any voltage is present, go to next step. If no voltage is present, go to step 17).
15. Repair open or short to ground in White wire between rear junction block and BCM. Recheck system operation.
16. Check for poor connection at defogger relay terminals. If connections are okay, replace defogger relay. Recheck
system operation.
17. Check for proper terminal contact at BCM. If terminal contact is okay, replace BCM. Recheck system operation.

Some auto parts stores sell a adhesive that has copper in it. made by "Permatex" just for that problem. Ask the parts guy.

check for power at the element on the window.

A common thing to fial on these- assumning the grid is ok, and wires are still attched to grid, is the rear def / antenna module. It is behind rt. rear quarter trim panel. The modules burn up, and also melt the connector. the module and connector would need to be replaced.

You can find Loctite Rear Window Defogger Tab Adhesive, at most major auto parts stores.
It's about a $10 repair kit. The instructions are in the pack.