There is a switch under the dash and in front of the brake pedal, ironically enough called the brake light switch. Basically the voltage flowing to the brake lights is on all the time the ignition is on, and the wire going from the positive source for this voltage flowing to the brake lights passes through this switch. This switch is usually white or off white in color. When you do not have your foot pushing down on the pedal, this switch is in the open position - that is it is NOT passing the voltage to the brake lights. When you push down on the brake pedal, this switch closes - that is it makes contact and allows the voltage to flow through the switch and then to the brake light bulbs. It is an interuptor switch, normally open but closed when you push down on the brake pedal.
Use a 12 volt electrical probe or a volt meter and make sure you have 12 volts to one side of this switch when the key is on. Then you should be able to see 12 volts on the other side of this switch when you press down on the pedal. If you don't have 12 volts at this switch when the ignition is on, the problem is with the source to the switch. If you have 12 volts at the switch, and you can get 12 volts on the other side of this switch when the pedal is pressed, then you have an open in the wireing going back to the stop lamps, or possibly in the circuit in the lamps themselves.
The lamps have a little bit of curcuitery built into them, and when they get as old as our cars are, this citcuitery within the lamps gets kind of funky. Mostly you get a problem with a lack of ground to or within the lamps, but since you say you have all the other lights working, then you should have a good ground to the lamps.
Personally, I wire in a secondary ground wire directly to a bolt or screw in the trunk somewhere, just to make sure that I have a reliable ground to the lamp assemblies.
check the fuses? i had the same problem. does your radio work?
i found a diagram of the fuse box layout and checked the one that said lights and it was fine. on a whim i checked some other fuses and one was shot .. replaced it and it worked fine. i think it was a brown fuse (7.5) after replacing it my lights AND radio both worked again.