If the break lights in my 1986 c corvette works but the tail lights do not, what could be the cause

The brake lights are controlled by a switch on the brake pedal arm. The switch needs to be adjusted or replaced, if the stop lights don't work.
Tail lights are on fuses as the other guys said.
Hope this helps.

There's a separate fuse for the tail lights.

How about the front park lights, do they work? The front and rear park lights, all are controlled by the head light switch. If none work, and you have checked the bulbs, it could be a bad light switch.

The brake and tail lights may share the same bulb, but they run on different filaments inside, so you could have a bright bulb on the brake filament, but the park light filament could be burned out. Look at the bulb closely to see. Any darkening of the bulb usually means a burnt bulb.

Blown fuse ,bad headlight switch,or wiring issue.
the tail lights have there own fuse and are powered through headlight switch. Do the front running lights come on? If none of them work, switch could be bad if front work and rears dont, check bulbs and power to them when lights are on