I've looked at the circuit diagrams, and there is a wire that goes from the wiper motor to the
BCU. This wire tells the
BCU that the wiper blades have reached the park position so the
BCU can switch the power off.
So the likely problem is that the
BCU thinks the blades are parked even when they are not.
To check, you need to check the output on this brown / light green wire using a meter at the wiper end. With the plug in and the wipers running, the voltage should change every time the wipers get to and leave the park position. My guess is the voltage should be low when they are not and go high when they are in park.
If the voltage is always low, then it could be a broken wire or bad connection between the wiper and the
BCU. If it's always high it's more likely the switch inside the wiper motor, although the switch could also make it constantly low.
As a first step, check the connector for corrosion or broken wires. If you don't have a meter, see if you can borrow a wiper or get one cheap as it is the most likely point of failure, especially as Andy seems to have heard of this before.