right rear brake light won't work

Check for power and ground with a test light in the socket as someone applies the brake pedal, it could be a defective socket or corroded wiring/connection. This car has a few years on it, so a worn socket would not be out of the question. Did you check all the fuses?

LOOSE GROUND WIRE ON LAMP ASSY. I FOUND THIS OUT ON MY COROLLA AFTER FAILING INSPECTION. YOU PROBABLY HIT THE GROUND WIRE LOTTERY.