Sounds like the park mechanism in the wiper unit, its usually a contact setup (or used to be when I last stripped one).
They keep the motor turning to a set point on a crank in the case, and then it cuts off the power and it stops
If you can get then unit out, its possible that the contacts could be fouled up, but more than likely they will be shot. It will work ok, you just have to park them on the stalk. Unless you replace the unit