1985 Toyota Camry Brake lights work until you turn on the headlights

These links show multiple fuse boxes and fuses which have something to do with daytime running light and lights.
Fuse box location and diagrams: Toyota Camry (1997-2001) - YouTube
Toyota Camry (1999 - 2000) - fuse box diagram - Auto Genius
1999 Toyota Camry Headlight Bulb Replacement, Relays and Fuses Explained - YouTube

Toyota Camry 2000 model headlight fault high beams not working xv20 Camry headlight switching off - YouTube

Toyota Camry Lights Not Working - YouTube

These Toyotas had daytime running lights. The headlights and the taillights turn on when you start the car. If you press the brake pedal, the rear lights (and the brake light in the rear window) should come on brighter.

I have never heard of the brake light staying on (The brighter filament in the two-filament bulb). Hope this helps.

Sell it, it's not worth fixing.

Instructions

Shift the Camry's transmission into park and rotate the ignition to the "OFF" position. Apply the parking brake.

Insert the tip of a small flat-head screwdriver between the dome light cover and the dome light housing.

Pry the dome light cover away from the dome light housing until it separates and pops loose.

Have you looked under the hood? There are more fuses under the hood. Is your dimmer turned down on your dash lights?

Are you saying that neither of the brake lights work or is it just one of them?

Will the headlights go out if the parking brake is applied?

on the brake pedal, there is a little switch, up under the dash, that controls the lights, replace that switch

check the headlight switch and also check the brake light switch on top of the brake pedal

Bad headlight switch or relay, or shorted wire. I would check the relay first.