I had similar symptoms.

In my case, there was an IC on the circuit board attached to the wiper motor that was fried. This circuit board controls all of the rear wiper/washer functions.

The damage should be visible when you take the circuit board cover off.

If you are adventurous, you can try to replace the blown IC (mc33286 iirc). Otherwise, you'll need to replace the whole motor assembly.

I doubt the stalk is the problem.

Good luck.