That is a good point on the violet wire.

Here is what I do not know about the wiper motors and maybe someone here will clear it up for us.

Where is that switch located that is pictured in the schematic above the motor with the park and run positions.

This might be the point where we need to start bench testing and seeing what works and why and why not.

I can see in the factory application where the DPTT double pole triple throw switch is using the thin violet wire to bring power thru the low speed side of the motor to park it.

Can you test your motor out with a 12v battery and some test jumpers to determine where this 3rd switch above the motor in the schematic is located physically.