Did you ever find out the real problem and remedy? We have an '05 LTD Roadster that because of Cancer, has been in and out of storage for 10 Years now (28,000) miles on it now.
Any way it started the EXACT same thing: Turn key on, no problems. But as soon as you start the car the wipers come on for 1 to 2 minutes, then suddenly stop at a random position. Other than this the car runs great.
Been starting the car once or twice a week, but with health issues going on it probably hasn't actually been driven this year.
Hope y'all know a sure fix by now. In the meantime I think I'll go put it on a slow charge for the night.
Thanks in advance,
Rotten