Windshield wiper "park" replacement

[m22mike]

Eddie is right. That coil is to activate the washer pump cycle, one revolution of the stepping cam. The wiper motor will work without this.
When the switch is turned off the motor runs until through a ground circuit that allows the motor to run until the park contact inside the gearbox is opened and the motor is then off. The park contact opens once every revolution via a cam on the gear in the box.
Have you bench tested the motor yet ? to see if it works . It maybe a good place to start. You should be able to find a good used or NOS pump assy.
In my drawing Hi speed dc volts is 12 not 2.
Mike