wipers will not turn off unless the car is turned off
Stalk is broken.
^
+1
I would say that–more than likely–the switch on the wiper/directional stalk is kaput.
Alternative guess/query – Is there is some gizmo on the wiper motor that keeps them running until they “park” (like the cam-driven switch of yore)? If that gizmo were shorted, wouldn’t the wipers keep running?
They stop oscillating first and then park.
It sure would look cool, however, of they kept going back and forth WHILE they parked! It’d kind of look like they were drowning.
Ah, right. I was thinking of the old kind that just stopped at the bottom end of the sweep, not the new kind that actually tuck themselves in.
Yes, I’d say if the PARK switch is broken, it might allow continuous running. None of my Hondas (up to 2010) “tuck themselves in.” I remember older GMs doing it. Which still do?
I seem to remember some BMWs having issues with a wiper relay due to the high current of the wiper motor affecting relay operation over the passage of time. This in turn would cause the wiper not to want to return home so to speak.
With German electrics poltergeists are also a viable option… 
just imagine a british luxury vehicle . . .
There is a wiper relay that gets stuck and causes the problem.