Turn signals quit

Sounds like your signal switch is probably working if you can get the brake light to turn off by activating for a left or right turn. Prime suspect is turn signal flasher, which is in a spring-metal holder clipped to the rear of the ash tray compartment in the dashboard.
I like to use the "electronic" flasher you can get at a parts store, an Ideal #EL-12 (or "EL-12C" is on a card instead of in a box).