Check electrical grounds
the turn signal switch is probably bad
Fuse
If you have the same bulb for brake and signal, brake light power needs to be interrupted by the signal lights, The brake circuit has to go through the signal light switch so the problem could be there.
This may very well be a problem with your ground connections at that turn signal.
Question: Does the turn signal blink on the right rear? I suspect not. Both the brake light and the turn signal use the same filament. If one is burnt out, the other will not work either. If so, the bulb needs replacing.
Answer Usually when the flasher blinks rapidly it's about finished. Try replacing the signal light flasher and see what happens. If you still don't have Brake Lights start looking for a short.
Since most brake/turn use the same filament in the bulb(1157) then if the turn signal switch is bad or offset then it will effect the brake lights.
Improper resistors.
Check and make sure you have the correct bulb. The turn signal/brake light is a dual element bulb and if you have a single element it does not work properly.
its a ground wire
Tail lights. Brake lights. Backup lights. Signal lights. License plate lights.
I would check the running lights for one with a short. I had the same sort of thing with my trailer and I spent way to much time troubleshooting the brake and signal wires. Turns out a running light bulb connector was grounding out on the trailer and messing it all up.