Check your fuses and circuit breaker first. Next, check the plug in wiring connecters. If the fuses are okay you most likely have corrosion or a broken wire in the plug in wiring connectors. A factory service manual for your truck would be a be help to you.
wiring Definetly sounds like a wiring issue. When you put it in gear and move even though its slight it is moving. Turn everything on and put your hand back there and just move all the wires around. If it does something try to narrow down which wires are shorting. if that doesnt work get a volt meter and check each fuse. Even though your fuse is good it might not be getting power. Try wiggling your fuse box around and your main harness.
Wires I think so man try ***** with all the wires while the truck is on. Get under the bed and check the wires going to the lights. Have someone help you so you know what going on inside the truck while you're doing it. I had the same problem on my Tacoma. I couldnt figure it out till i crawled under my bed and saw all my wires chewed up. My dog likes to sleep under the bed.I think it has to be grounding because the ac has a seperate fuse from the dash lights and its grounding the whole system. You can do an alternator check by removing the pos wire while its running but I dont think thats the problem. Let me know if you figure this out.
Yes, switch in the tranny... When you put it in reverse it turns on the reverse lights. Its sounds like it bad and grounding out that circuit... STOP fuse is for the brake lights...