[Flatrater]

I would bet you own a 97,98 or 99 GP.

I doubt that your first problem is related to your second problem. An ignition fault would cause a loss of power causing dim lights, or flickering lights and not a blown fuse.

You have a short in the system. If it was the ignition switch you would blow the fuse before the ignition switch and not just the tail light fuse. Since it only happens when you shift into reverse I would look at the reverse light, making sure the bulbs are correct and that the wiring going to the lights isn't pinched causing your short.