First off details on my truck:
So I thought maybe it was an electrical issue and my GPS has a battery backup so I kept it unplugged but turned on GPS on battery and once again it did it.
So it was unplug from the lighter and when you turned it on, on its battery, it still turned the wipers on?
I wonder if when its on the signal it sends and receives for the location is raising havoc with the computer, or some other system in the truck?
My daughter had one of those cheap technecs (spelling) kids toy lap tops and when ever she turned it on it would make the 86 Burb run like crap, the truck would actually knock and ping. When she shut the thing off the truck ran fine.
So needless to say she never was allowed to use it anymore in the truck.
I think it had some sort of leak in the radio frequency range that screwed with the electronics of the truck.
I wonder if you could be having a similar problem.