OK. I see what type of motor you are using. I did not see a schematic anywhere on that link, but based on what you told me, it probably looks like the attached (Standard Wiper).
If this is correct, then it probably operates just like DaveMcK38 describes, when the wiper switch is turned to "Off", power is applied to the park circuit, and the motor stays energized until the wiper arms reach the park position, and the internal switch opens.
Been sitting here thinking for awhile, and I think you guys are correct about a second relay. Can't really come up with a solution without adding one.
One suggestion (other attachment) that might make your life easier, would be to use a double throw relay - like in the circuit provided by klhansen. If you had power on the relay common, you could connect the park circuit to the NC contact, and the low circuit to the NO contact. That way, your pulse circuit would only have to energize the relay long enough for the motor to move enough to close the park switch, and you could then just let the motor handle the rest of the wipe cycle.
The second relay comes into play in order to isolate those circuits under normal operation. I suppose you could also use a 2 pole selector switch that would do the same thing, but I know some of those can get rather expensive and kind of large in size.
klhansen,
That's an interesting circuit. It looks like the use the "Run Park" relay for motor activation, and the "High/Low" relay for speed control. The park switch looks like it has two jobs, one to keep the motor running until the wiper arms make it to the park position, and the other to signal the controller (GEM), that the motor is parked.