Buick 1998 Century My left rear brake light does not work when brakes are applied. All other brake lights work. I tested the circuit with a meter and when the brakes are pressed the circuit shows 13-14 volts. The blinker works OK and uses the same wire as the stop. Light is new and works on the other side.

test your brake light switch

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 .

best way is to remove lenze and get to bulb with a test light connect tester lead to power and test bulb wires with brake lights on and you will prove your ground is working also autozone library has a very good section on this

Do you know how to do automotive electrical testing ? How to use a DVOM - digital volt ohm meter ? You have high resistance in the circuit . Use voltage drop to find the problem .
Mastering Voltage Drop Testing with Pete Meier and Jerry Truglia

there is a seprate ground that mounts to the frame of your car near the light usualy in trunk in between the rear speakers locate and make shure the conection is good.if that dos not solve it on the pasengers side rear light check bulbs for detereated ends if thay are then replace.this shuold solve you problem

If you have power thru the brake light switch, the next component to test is the turn signal switch. If the regular brake lights and turn signals are on the same circuit they both go thru the turn signal switch.

With a 12 volt test lamp check for power at the lamp socket. With the test light properly grounded it should flash like a turn signal. If you have no power at the socket you have an open circuit (broken wire or bad connection). If you have power at the socket you have a bad ground.

yes, on multiple electrical problems like this the first thing is to check the ground circuits, in you case focus on the left rear

No Diagram. You either need brake work or have a blocked rubber hose or caliper,on the left side and all the braking is taking place on the right. Very old vehicle,so expect these issues.

have you bled the brakes? If you have, you may need to do it again as there sounds like there's an air lock in your lines.