Could it be the motor which has a set of contacts to detect when the wipers are in the "parked" position? Wipers keep running until parked after being turned off, if the contacts are faulty it may just keep going. Has the car had a recent windscreen wiper freezing event?
I would agree with a motor faulty too.
Wiper motors have (or certainly used to have) a permanent live for the purposes of self parking. This would tie in with the wipers working irrespective of the switch position. As the motor doesn't know that the wipers are parked, they just run indefinately.
The power to the permanent live will be getting cut some seconds after turning off the ignition, due to the battery saver function cutting in. This will be causing the wipers to stop.
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