1999 Dogde Caravan rear wiper starts running when vehicle starts, switch will not shut it off

Most common cause is the very trouble-prone Body Computer. It's real hard to get out. It lives above and ahead of the brake pedal. It's plugged into the fuse box and is held on with three 5/16" head bolts.

The control assembly around the radio can cause this too. Typically if it is the cause, the yellow light in the button won't turn off.