My specialty is electrical, I had a similar problem with my brake light as well, the only difference is mine would only work if the pedal was depressed and pushed to the left. My problem turned out to be a terminal that backed itself out of the connector.
Do you have a multimeter? If yes, your life will be 10 times easier. If no, get ready for a lot of trial and error. The center mount stoplight if I remember right is fused with the other two brake lights.
If you have a multimeter, depress the brake pedal with something or someone and verify that the two working brake lights are lit. Then take your miltimeter and probe between each side of the bulb socket and a ground. For ground you can use any unpainted metal, or take a jumper cable from the negative battery terminal only to where you are probing as the ground. Do not hookup the positive side of the jumper cable. If you get voltage around battery level then the positive is connected and probably working. Then you are going to want to take and switch your multimeter from volts to ohms and probe between ground and the negative side of the socket. If it reads anything over 10ohms or OL you have a bad ground. and will either need to track it down or replace it. If you dont get voltage you will have to goto the brake light switch on the brake pedal and check for loose connectors. I dont know where the wiring splits to the three lights however so you will need to trace this, the lighting circuit is the right two most wires if the plunger is facing the right.
If you dont have a multimeter, get yourself a testlight they are a few bucks at an auto store, without something you will not get anywhere fast as you have no way to tell where the problem is. If you are in a real pinch, any 12v light with two jumper wires will work, just dont light it for too long or it will get too hot to handle.
Tracing the wires is the hardest part of the job, but if you want to forgo that you can just say **** it and run new ground/supply wires, just make sure you label them should you ever go back and wonder what that wire is to.
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