1987 rear brake lights stay on with the ignition switch off.

Usually behind brake pedal... The switch probably isn't faulty. Have you gotten your brakes replaced recently? Are they old and worn? If your brakes are old and/or your fluid is low, there is sometimes not enough pressure in the system to hold the pedal all the way up, so sometimes the pedal sinks down a little and activates the switch.. Try topping off your brake fluid reservoir.

Thank you. I will have to check that. It is a car that a neighbor is planning on giving me and I haven't had a chance to dig into it yet.

Check and replace broken/missing plastic bumper between brake armature and brake light switch. The part is a couple of bucks at the parts store. The tools that you need for installation are one hand to hold brake down while the other hand inserts bumper into place. You didn't need to replace the switch, just the plastic part that gets beat on every time you step on the brake. Who'd a thunk it?

I have the same problem. The brake lights in my 93 Toy Tercel stay on constantly, even when the key is removed. To turn off the brake lights, I need to remove the fuse. When driving the car, the brake lights are always on. The brake pads are about 2/3 full and there is the proper amount of brake fluid in the reservoir. Recently, I replaced the switch behind the brake. My next step is to check the switch again and to look for shorts in the line. One would think that pushing the pedal triggers the switch that sends positive current to the rear brake lights.