Educated Guess - the 'Parking' contacts on the wiper motor are
getting wet or corroded and are shorting together, starting the motor.
Or the cam is getting worn to the point that the contacts are closing
on their own.  The solution could be as simple as cleaning up the
switch or adjusting the gap by bending the contacts.

 Wiper motors have 'Parking' contacts so even if you turn off the
switch mid-stroke the motor keeps running till the wipers get back to
the bottom, then a cam from the wiper arm output shaft opens the
contacts.  If you have turned off the stalk-mounted wiper control
switch, they stop every time they reach that point.

 If your car has wipers that visibly stop at the bottom of the stroke
and then retract below the cowl line, it's the same idea but a lot
more complex - I think after they stop in the normal parking position
they reverse the wiper motor to get the arms to retract into the final
parked position.