I recently noticed that when I hit the brakes, the white reverse light lights up along with the brakes. Nothing has been rewired so I don't understand how this could have happened. Any ideas?

 

Three questions -
1 - does the brake light come on when you press on the brake pedal?
2 - what lights come on when you put the car in reverse?
3 - do the lights on the front of the car work properly?

 

this usually happens when a bulb that was recently replaced (even elsewhere, for example, turn signal bulb) is incorrectly installed in its socket.

 

Sounds like you used the wrong bulb. Reverse lights are usually single filament, if I'm not mistaken they should be bulb # 1156 while brakes might be 1157 which is dual filament. Check that and if not, at least make sure you put the bulb in right and not forced

 

the interesting part is that this guy has started this thread and has abandoned it, leaving the rest of us to discuss theory and what if's. There isn't any logical connection between brake/tail lights and backup lights even if the wrong bulb was used. I think there is a wire harness problem where something is cutting into the harness and shorting the brake and backup wires together.