Front left element indicator light will not go out

There should two separate bulbs for marker and blinker. It sounds like a bulb is burnt out, bad ground, melted socket or a wiring anomaly. Are you certain it's supposed to have 57 series dual element bulbs for blinker and markers?

Looking at a wiring diagram for the passenger seat an checking wiring colors mite help you figure it out . But then again maybe not . Electronic's involved here , Right door module .
Heated Seat Components
The heated seats consist of the following components:
• Left heated seat switch
• Right heated seat switch
• Memory seat module
• Left door module
• Right door module
• Left seat cushion heating element
• Left seat back heating element
• Left seat cushion temperature sensor
• Right seat cushion heating element
• Right seat back heating element
• Right seat cushion temperature sensor
Modes of Operation
The heated seat module (MSM) controls heated seat operation for both the driver and passenger seats. There are 2 modes of operation available for heated seats; both the seat cushion and seat back heat, or seat back only heat. When a heated seat temperature signal request is received, the MSM will activate both the seat cushion and seat back heating elements. When the heated seat BACK ONLY mode button is pressed once the MSM will deactivate the seat cushion heating element and leave the seat back heating element ON.

Heated Seat Switch/LED Indicators and System Operation
The left and right heated seats are controlled by separate heated seat switches located in the door panels. Ground is supplied to the heated seat switches through the switch low reference circuits from their respective door modules. The door modules also control the heated seat switch heat mode and temperature indicators. The memory seat module (MSM) controls the heated seat operation for both, the left and right heated seats.
The following describes the sequence of operation and how the MSM responds to each of the switch inputs.
• High Temperature--When the heated seat switch is pressed once, ground is applied through the switch contacts and the switch signal circuit to the door module indicating the high heat request. In response to this signal, the door module applies a low current voltage through the 3 temperature indicator control circuits illuminating all 3 LEDs indicating the high temperature mode. The module then sends a message via the GMLAN serial data line to the MSM indicating the heated seat request. The MSM then applies battery voltage through the heating element supply voltage circuit to the seat cushion and seat back heating elements. At the same time, it supplies a ground through the element low reference circuits to the seat heating elements.
• Medium Temperature--When the switch is pressed a second time, the MSM sets the temperature level to medium heat. The door module removes the voltage from the high temperature indicator leaving 2 LEDs illuminated indicating the medium temperature mode.
• Low Temperature--When the switch is pressed a third time, the MSM sets the temperature level to low heat. The door module removes the voltage from the medium temperature indicator leaving 1 LED illuminated indicating the low temperature mode.
• System OFF State--When the switch is pressed a fourth time, the MSM removes the battery voltage and grounds from the heating elements. The door module removes the voltage from the low temperature indicator, indicating the system OFF state.
• Back Only Mode-When the heated seat is ON and the BACK ONLY mode button is pressed, ground is applied through the switch contacts and the heated seat back only mode signal circuit to the door module. In response to this signal, the door module sends a GMLAN message to the MSM indicating the back only mode request. The MSM then opens the ground path to the seat cushion heater element, leaving the seat back heater active. The door module turns OFF the seat cushion/back mode indicator, then applies a low current voltage through the heated seat back only mode indicator control circuit illuminating the back only mode indicator.

Know how to test an what test is the key to finding the problem .Not guessing . The connector you found may or may not have anything to do with it . What color are the wires ? I have factory service repair manual . Does it have memory seats ?
The Memory Seat System consists of the following components:
• Memory seat module (MSM)
• Seat horizontal motor
• Seat front vertical motor
• Seat rear vertical motor
• Seat recline motor
• Lumbar horizontal motor
• Seat horizontal position sensor
• Seat front vertical position sensor
• Seat rear vertical position sensor
• Seat recline position sensor
• Lumbar horizontal positional sensor
• Seat adjuster switch
• Seat lumbar switch
• Memory seat switch
• PWR SEATS Circuit Breaker 30 A
• MEMORY RPA Fuse 7.5 A

no fuse. Probably the element.

This is the multifunction control module. Whne you look at the fuse box, you are really looking at a computer ie... the multifunction cotrol module. Everything goes thru this, except the ECM.

Replace both sides with correct dual element bulbs which may be the culprit here

mvek,
If you could see through the glass, you'd see "temperature sensors" located near the elements. They're very sensitive little guys, and rightly so! Their job is to detect temps and energize the warning light on the cooktop so users won't get burned.

To answer your question... It appears that there is an issue with the front left sensor (and possibly the right as well). The temp warning lamps should NEVER go off immediately. Please call for warranty repair (1-800-GE-CARES). This is an unsafe condition for you and your Family. The warning indicators are there for a reason and should indicate high temp's as long as high temp's are present.

SG

Usually when your signal blinks rapidly it indicates a blown bulb.   Switch on your four-way flashers and check your bulbs at each corner.  On the brake light staying lit, check to see if the left-rear bulb is installed correctly and is the correct bulb for the application.  I've seen people force bulbs in sockets causing the braking element of the bulb to light instead of the parking element.  The braking element is much brighter than the parking element.

timer on what ? make, model and age of unit might be useful in forming a coherent response.

if the indicator lites up replace the element the sensor is probably bad you can take a small screwdriver and pry the connectors loose safely btw the sensor is the rod running across the element