9 times out of 10 when wipers do not park, it is a bad wiper motor. There is an internal switch in the motor that constantly closes and then opens when the wipers reach the cowl (park) position. This internal switch is by-passed by the dash switch to keep the ground circuit closed and wipers "on". When the switch is off, the by-passed ground path is opened, the wiper motor switch contacts remain closed, and the ground path remains closed, the wipers continue to operate until the wipers reach the cowl position then the contacts open and the motor stops.....
....in theory anyway....
You didn't say what happens when just the wiper switch is turned off... Do they stop regardless of position?