Wiper Motor Park Not Activating

Here's an issue that I've investigated and googled a bunch- I think I know the answer, but want to check with everyone here to see if there is something obvious I am missing...

My Series 3 has the Lucas 14W 2 speed motor and the rotary two speed switch that you push to wash the windshield. It was never wired to the switch correctly when I got the truck, so I took the time to get all connections on the back of the switch correct, and verify that all wires to the motor are correct. The switch is NOS from Ike.

When the motor is in the "Off" position, it runs on low. It runs on "low" in the "low" position, and "high" in the "high" position. If I turn the wiper switch to the "Off" position and pull the park switch off the motor and press down the button that should engage the gear cam, the wipers stop. This tells me that the park switch is not engaging on the cam. I have a constant 12V from the green wire to the motor....

I've messed around with the gear housing a bit and tried two different park switches that test good on the bench. It's clear that there's just enough slop in the gear motor to keep the park switch from being pressed enough, the cam on the gear is worn down (doesn't seem like it?), or the gear I have is wrong.

Has anyone experienced this before or know of a way to get the cam on the gear to engage? There's grease all over the cam for lubrication...perhaps there should be none? Or is it time for a new motor and gear?

Let me know if this makes sense or if you need clarification. It's not often the Prince of Darkness stumps me, but this one has me losing hair.

bump? Anyone?

I have a one speed/earlier model wiper motor (runs both wiper blades) that I believe operates the same way.

Basically you have two power leads into the wiper motor - an "always hot" lead (that is on the same circuit as the horn) - and - a switched lead that is controlled at the dash. There is a circular cup/disk that spins around and around in the motor with two sections on it (think of a pizza with only one small slice cut into it). One section is always hot/on. The smaller section is on/off via the switch at the dash. There is a contact that draws power for the motor off the disk (like a record needle). If you shut off the smaller section at the dash/switch, the wiper stops rotating when the "needle" hits the dead/unpowered section and "parks" the blades. Switched on at the dash - the entire disk is live and the wipers go through full sweep. You can adjust the disk to to determine where in the cycle the blades park...