Brake lights

I too have the same exact problem. Same Car. (2000 Pontiac Gran Prix - mine is GT model 3.8uL V6)Just started about a week ago.
The 3rd brake light works perfectly.
The turn signal works perfectly (I believe that the turn signal and brake light share the same bulb element / wire).
When I hit the brake pedal - there is no power to the brake light.. I tracked the wiring down to the giant tube of wires going into the back seat - ground to the bulb is just fine. I was hoping that someone could tell me:

1) Do the turn signal and brake lamp share the same bulb filament?
2) where is the relay / sensor where the brake lamp gets its power from?\

I believe it has nothing to do with the brake pedal switch as the 3rd brake light works just fine.

Try wiggling the hazard button and see if you get any changes. The hazard stem melts to the multifunction switch body. The hazard switch may be under recall, but the problem is likely the multifunction switch.