In the good old days, when God was still a lad, wipers didn't self-park. When you turned them off, they stopped so, to avoid having them block your view when off, you had to switch them off when they were out of the way.
Then the self-parking wiper was invented. As the wiper motor starts to turn it operates a switch which connects power to itself, thus keeping the motor running even if the wiper switch is turned off. When the wiper arm is in a tidy position this connection is broken. If the wipers are still switched on the motor continues to run, otherwise it switched off.
The chances are that this connection is not being made on your car, probably due to either water ingress or a bad connection somewhere. If you can get to the wiper motor have a good look at the connections on it. Otherwise try to open up the motor and look at internal connections.