It might be with the dash switch but more likely is with the windshield wiper park switch, And, here is a surprise, it might be in the wireing harness.
There are a few different ways wipers hook up but one method has 2 power lines, one goes to the switch and then on to the motor, and the other goes direct to the motor, it is connected to the park switch, thus when you turn off the wipers this switch is closed and remains closed till the wipers reach the closed position, and then it opens and shuts things off.
If this 2nd power lead is disconnected, broke, otherwise damaged instant "PARK"
Connection method 2 has the dash switch switching between motor high/low/park leads
Connection method 3 uses a control box (This one may have timers and such in it)
And I'm sure there are other methods as well
But my guess is the park switch, it's part of the motor