Bentworker's post in Wipers spontaneously started working, but they get parked in the up position. was marked as the answer
Kinda sounds like the arm was installed 180 degrees out on your wiper motor if they park in the full upright position.
Bentworker's post in Windshield wiper park when switch turned to off? was marked as the answer
After asking the question I went out in the garage and figured it out.
Discovered that the wiper motor gearbox has a cam that pushes a rod that breaks a contact inside the motor to make it park. A flat spring returns the contact to position. The rod having 50 year old grease wasn’t freely returning. Got that all cleaned up and put some fresh lightweight lube and it is working great. The wipers park perfectly.
If your wipers won’t park and you go down the same avenue I did the only advice I have is that the wiper motor is a DC Permanent magnet motor, so if you decide to remove the two screws with a 5/16” head and remove the cover it will try to take the rotor with it (because of the magnet). Since there are carbon brushes on the rotor it would be easier to not make the same mistake I did. If you take off the gearbox cover you can use something soft like a small piece of wood or plastic to put pressure on the worm gear, and that should keep the rotor in place while you remove and install the cover.
Red circles show where the cam lever, pushrod and contact are.
Bentworker's post in Repop deluxe dash panel - how did you secure it? (They made the mounting posts smaller) was marked as the answer
Well- the self 5/16” self threading nuts worked. A little tight for my taste so I took a chainsaw file to them to remove a little material. I ended up drilling out the screw holes a bit as even with the slightly smaller screws I got from McMaster I was still a little uncomfortable with the fit.