Probably either a bad brake lamp switch, improper adjustment of the brake lamp switch or a bad turn signal switch.
The brake lamp switch also contains the cruise disconnect switch, but often only the brake lamp portion will fail due to the higher current involved in running the brighter lamps. The switch develops resistance caused by carbon tracking on the contacts from the spark that's created whenever the switch changes states.
Also, the brake lamp circuit runs through the turn signal switch. If the brake lamp contact in the switch goes bad, you can have a situation where the brake lamps won't light but the turn signals function properly.
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.
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.
This may very well be a problem with your ground connections at that turn signal.
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.
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.
Improper resistors.
its a ground wire
Tail lights. Brake lights. Backup lights. Signal lights. License plate lights.