Would fuse cause rear brake lamp and turn signial to stop working ? change bulb did not help

id say left side ground is bad (rust)
car is plastic so grounds must good.
fuse checked first
see if scans show BCM errors
inspect socket for damage or rust
make sure the ground wire to it really is grounded
using the correct bulb # seen in the now lost users guide?
the guide is free in USA, if are.
it says stop tail turn is 3057
do that? and not LED upgrades okay,
again I only do USA cars. not exports to say UK or others.
RR, right rear is ground named G401 (same for stops)
the wire is black solid black
is center rear stop lamp dead too, it uses G401 too
LR side uses G101 ground
now the big clue not told
is park lamps dead. tool.
the whole rear of car lamps park and license and side markers all use G401 so if those work then ground is not bad.
question #2 are Hazards failing rear.. fuses must be good.
we check all fuses on cars with any kinds of electric failures.
but if fronts work
the hazard and all turns fuses are good and the flasher too,.
there is no REAR fuse, fronts and rears 2 fuses
fuse HAZt/SG-#15
STP-HAZ #8

THAT IS ALL I COVERED IT ALL
THE TESTS ABOVE PROVE THE PUDDING
WHAT ALL OTHER LAMPS DO MATTER. HUGE HERE.

• STOPS
• TURNS
• PARK
• HAZ MODE.
• EVEN REVERE USED G401 TOO

MY GUESS
WRONG LAMP ,CORRECT IS 3057 TURNS
GROUND JUST TO DEAD LAMP CUT BUT NOT OTHERS.
SOCKET TOO LAMP BAD (RUSTY CONTACTS)
A VOLTMETER FINDS IT.

Check the wire grounds where the lens connect to the vehicle. With a test light check to make sure current is arriving at the bulbs. If not, then follow the wires back to the light switches.

Light bulbs require power and ground in order to work. The ground circuit for the left rear combination lamp is shared between the turn lamp, stop lamp and tail lamp. Because the tail light still works in that specific combination lamp, we know that the shared/common ground for that assembly is OK. The power circuit for both stop lamps (left and right) have the same origin; voltage flows from the STOP LP FUSE (15A) through the DBC RELAY (when the stop lamp switch is pressed) and then to each stop lamp via their respective circuit branches. Because the right stop lamp works, we know that the shared/common fuse, relay and switch are all OK. I'd suspect an open in the left stop lamp power supply branch and would recommending checking for voltage on the green & black wire at the left rear combination lamp assembly to confirm. Regarding the left lamp on the hatch, the wiring diagram indicates these are not stop lamps rather tail lamps only. I'd recommend installing a tail lamp bulb instead of a brake light bulb into that assembly as a first step. You can read more here: https://www.yourmechanic.com/article/how-to-replace-your-car-fuse-box-by-jessica-howe

Stop Lamps
The brake pedal position sensor is used to sense the action of the driver application of the brake pedal. The body control module (BCM) provides a 5-volt reference voltage and low reference to the brake pedal position sensor. The position sensor provides an analog voltage signal back to the BCM that will increase as the brake pedal is applied. When the brake is applied, the BCM will then apply battery voltage to the left and right stop/turn signal lamp supply voltage circuits and the center high mounted stop lamp (CHMSL) supply voltage circuit illuminating the stop lamps. At the same time the BCM applies battery voltage through the signal circuit to the transmission control module (TCM) and the engine control module (ECM) indicating that the brakes are applied.
Ground for the stop lamps is supplied as follows:
• G402 provides ground for the left rear stop/tail/turn signal lamps
• G403 provides ground for the right rear stop/tail/turn signal lamps
• G301 provides ground for the CHMSL
The stop lamps on this vehicle will not illuminate unless the ignition is in the accessory, run, or crank positions. When the ignition is in the OFF position the stop lamps will not illuminate when the brake pedal is applied.
Battery voltage from the LT TRN/SIG and RT TRN/SIG fuses located in the rear fuse block is also used by the body control module (BCM) for stop lamp operation.

Turn Signal Lamps
Battery voltage supplied to the body control module (BCM) from the fuses listed below is used for turn signal and hazard lamp operation.
• LT TRN/SIG fuse for the left turn signals
• CTSY/RF TRN fuse for the right front turn signal
• RR TRN/SIG fuse for the right rear turn signal
When the turn signal switch is place in either the LEFT or RIGHT position, ground from G300 is applied through the turn signal switch signal circuit to the BCM indicating the turn signal request. In response to this signal, the BCM applies a pulsating voltage to the front and rear turn signal lamps supply voltage circuits cycling the lamps ON and OFF. At the same time the BCM sends a GMLAN serial data message to the instrument panel cluster (IPC) to cycle the appropriate turn signal indicator ON and OFF.
Ground for the turn signal lamps is supplied as follows:
• G104 provides ground for the left and right front turn signal lamps
• G402 provides ground for the left rear stop/tail/turn signal lamps
• G403 provides ground for the right rear stop/tail/turn signal lamps

Do you have a factory scan tool (tech2) ? Your best bet , take it to the dealer .

Did you check STOP LP fuse 15amp. in the rear fuse block ? Do you know where this is. Fuse Block - Rear Under the rear seat, on the left side of the floor pan.
The STOP LP fuse in the fuse block - rear supplies battery positive voltage to the normally open stop lamp switch. When the driver presses the brake pedal, the switch contacts close. The battery positive voltage flows to the left stop lamp assemblies, to the right stop lamp assemblies and to the center high mounted stop lamp (CHMSL). The left stop lamp and the CHMSL have ground at G402. The right stop lamp has ground at G401.
Did you check for power at the stop lamp switch ? both in an out of the switch with brake pedal pressed ?
Did

bad earth the wire that goes to the car body could be lose

{: ) Check out the ST/LP fuse(25amp) at the underhood fuseblock. Also the VEH STOP (15amp) and VEH CHMSL (10amp) fuses at the fuseblock rear. If the center high mounted stop lamp is also not working, and you can't get any 12volts on either stoplamp bulb sockets, then most likely causes are the fuse, stoplamp switch on the brake pedal, and a faulty wiring.
If the center stop lamp is working and both sides are not, then the trouble can be isolated on the wirings or terminals of the two bulbs on the sides.
Wish you luck.

it may not be that relay. if this happens when the vehicle is idling. look under the dash at the fuse panel. put your finger on each relay. you will feel it if it's the one that is clicking. replay the offending relay.

You may have some wiring 'grounding' problems in the areas of concern. Remove each connection, and clean any rust. Place a light film of grease and a fresh star washer next to ground point, then the wire connector and other washers. Tighten firmly. Check the lamp sockets for any corrosion and replace same if found. The front lamp flashes rapidly because the rear light not working causes the flasher unit to switch faster.

are the rear lights combined? ie sidelamp and brake lamp in one bulb .if so, there is a possibility that the bulb is not sitting correctly in the holder , causing both the side & brake lamp fuses to blow . if they are seperate bulbs you probably have ashort in the sidelamp system somewhere but the brakes could be a switch problem [easy check, find switch ,disconnect wires short across using wire or paperclip switch on ignition and check lights ] if they work the switch is the problem , [check fuse first] if they don't