I used to have a 1990 Winnebago Chieftain and I also had some wiper issues. I would suspect that since my old Chieftain and your Brave are only 2 years apart and both on a P30 chassis that they have a very similar setup.
My issue was that my wipers would just randomly turn on. Over time, it got more frequeent - to the point where they would be on almost all the time. I could turn them on and they would stay on as they should. But, when I would turn them off, they still would randomly come on. Unfortunately, I never did fix it. I did notice a noise that would occur when it would kick on and off. It sounded like a small relay kicking on and off and it was definitely associated with the wiper coming on and off.
I traced the noise to the wiper control module - which is in a silver box on the wall underneath the dashboard. I never did get around to pulling the unit to check it out. About the only thing I ever did was disconnect it - which meant the wipers didn't work. It was a pain to get to and disconnect. But, I would suspect you are having issues with the same control unit. I never was able to find out who made the unit nor where I could buy a replacement. As such, I never got around to doing much about it.
My solution ended up being to remove the fuse (which was more like a small relay than a fuse) in the fuse block under the hood (driver's side). Like disconnecting the module, it turned off the wipers completely. But, it was easier to reconnect than the under-dash control module. I then used RainX before any trips and I didn't have to use the wipers. If I did have to use the wipers, it was easy enough to pop the hook and put the fuse/relay back in place.
2001 Bluebird Wanderlodge LX ME