Brake Lights Don't Work
Without doing a "hands on" troubleshooting of your vehicle, no one can tell you what specific defect is causing your problem. Therefore this answer will of necessity be of a generic nature.
Usually this type of problem is caused by what is called an "open circuit" condition.
Open circuits can be caused by onr, or more of, several things, a few of which I can recall now:
Because it's only the brake lights I would first make sure the brake light switch is properly adjusted.
If that's not the problem, then fully inspect and check the wiring harnesses and ground wires and connections for the brake light circuit.
The "proper fix" is for someone who knows what he or she is doing to troubleshoot the nonfunctional circuit, find and identify the defect, and properly repair it
Check the brake light switch located under the 1989 Toyota Corolla. If the switch is stuck the parking light will continue to stay on.
change the brake lights check the fuse check the brake light swtch
Check the radio/Acc fuse...
Check the bulbs, the fuse and the brake light switch.
Blown fuse? Bad stoplight switch? Open wire to brake lights Not ground at brake light sockets? Problem in steering column (turn signal circuitry)?
Replace the brushes in alternator. refer to the haynes manual on how to do it.
It plugs into the taillight.
Either your emergency / parking brake is on or your brake fluid level in the brake master cylinder in your engine compartment is LOW
Check bulbs, fuse, bad ground, brake light switch.
adgust the brake light switch at the brake pedel under the dash
Please re-phrase your question; it appears you are saying the brake lights come on when you push the brake pedal and the lights are working (normal operation). If the lights are staying on after you release the pedal, then the problem is with th brake light switch (sticking). Thanks Malcolm
chek the switch on top of steering column