Sounds like it's not your bulb that is bad. It may be your brake switch isn't working.
The only thing common to all those lights (but not to the center brake light) is the hazard switch. I'd check that next. On my 96 Century the hazards override the signals and brake lights meaning that the signals and brake lights must be wired into the hazard switch somehow.
Check your tow bar and trailer brake light wiring. It may be grounded. I had this problem with my 92 roadmaster wagon. Tom.
How do you replace brake lights
I have a chev cavlier 1995 and the running lights do no work---on the dash the green light keeps blinking----what should I do?
I have 05 with no brake lights
Buy the Chiltons or Haynes manual. It will walk you through the process.
It depends on the vehicle but in general you would have one fuse for the signals and one fuse for the brake lights.
Brake lights
I had the same problem with my 87 Riv. It was a burnt out bulb in the rear of the car. My front signals did work and as they run on different circuits, check and replace the bulbs. Access to the back lights are inside the trunk back.
Fuse 7 controls the brake lights. It should be a red 10amp fuse.
you probably have a bad ground in the rear taillight assembly common problem
Blown fuse