1992 toyota corolla tail light problem

The first thing to do would be to clean the socket real well, and make sure no corrosion. The brake filament pin may be corroded up and not making contact with the connection on the bulb. Also make sure no ground problems to the light housing if it has more than one bulb. In some cases, it can also be a bad bulb. Could also be a break in the brake filament wire to the housing. I had a old Chevy once with aluminum wiring that corroded easily if any water got in the trunk, which that one did. The wire would eventually overheat due to the extra resistance and finally go kaput. I'd then have to cut to clean wire and reconnect. But I'd clean the socket and pins real good first. You could also use a volt meter from the two pins to ground after cleaning to verify if it's actually getting power at that point. One should be hot with just the lights on, and when you press the brake, the other one should become hot, and the other one go out, which is why the lights go out when you press the brakes. Your regular light pin is OK, but the brake light pin is not for some reason. Usually corrosion most times.

You have a bulb that is burnt out. Turn the lights on and test again.

HINT You can test by yourself by backing your car near an office building with windows at ground level. You can see the reflection of your lights in the window. Of course, you can use a helper to work the pedal and light switch.

Check the grounds.