I took it to the dealer and they weren't able to reproduce the problem, so no fix was attempted. I've seen other cars without a wiper for the back window, but the knob the wiper was supposed to be on was turning back and forth. Now I know why. This is completely irritating.

If I turn on the windshield wipers, the wiper on the back window also turns on. The back wiper control is in the off position and the wiper doesn't respond when the control is used during this time. It sometimes stops after several minutes and then it will respond to it's own control..