Help! Reverse light problem

[rusty ol' 69']

The reverse lights don't seem to work on my truck. First, I tried the obvious--busted bulb one side and no bulb in the other--so I replaced the bulbs. Now, when I hit the brakes the reverse lights come on. Since I'm feeling lazy I figured I'd ask before I started digging around. Here's my question, If I replace the backup switch will this solve my problem, or do I need to stop being lazy and follow the wire back to see if it's just hooked up to the brake lights? It would seem that their just hooked up incorrectly to the brake lights, but I just wanted some opinions on the matter.

Thanks and Happy Turkey day!

Kevin