Do you have a multi-meter?
The other thing to check would be the brake light switch above the brake pedal, if you can get a wiring diagram you could verify it has a good ground, and that when you apply the brakes there is 12v coming from the wire that turns the brake lights on.
I am not sure why the reverse light is not working though, unless it is a maxi fuse under the hood, and they are both tied to that fuse.
If it is blown then you may have a wire grounding out somewhere causing it to blow, I wish I could be of more help, I will try to search for a diagram, not sure if I'll be able to find one though.
2006 Pontiac Grand Prix GT with SC
1996 Buick Park Ave NA