why not pull the fuse and put a tester on it to see if there is a grounding issue. That is the first simple way to check it. It sounds like there is a ground issue and when reverse is activated, the lights come on and it blows the fuse. I have found it does take a few seconds at times to blow a fuse. I would bet the wires have rubbed something and are bare. How do I know? I probably pull a trailer behind my truck twice a week and have dealt with mice, road salt, vibration, etc all causing a simple bare spot. Yes I know he has a class A but light wiring is pretty much the same. Fixed one trailer 5 times before I finally rewired it and found I had a mouse apartment house in the trailer frame and I was catering their meals with the wiring.