Been a long time since I worked on wipers, but as I recall there is a control switch mounted on the motor that has a landing area with no electrical contact.
When you shut the wipers off from the switch, the motor continues to run until it gets to that landing zone, which corresponds to the physical position you want the wipers to stop at. When the switch is on, it effectively bypasses that landing zone circuit so they keep running.
Some cars that had hide-a-way wipers used to actual reverse the motor when you shut them off and that would pull them down under the edge of the hood. Our trucks don't have that feature though.
I think the thing to look at will be near the motor/linkage connection if you can get to it. Could just be dirty/corroded inside and cleaning it up will fix it. If that switch is gunked up, the motor won't keep getting power when you shut the switch off to finish seating the wipers. The wipers are running on switch power only, and not the parking circuit. Look for where the wiring harness connects to the wiper motor. You will see that the wires don't go directly to the motor hopefully. They go to a little control box that is then wired to the motor. If you can find what I'm talking about, clean it all out. Your liable to find old black looking grease in there. Get it out and relube it with dielectric grease.
I've never done this on a RAM, so be aware you may need to remove the wiper motor to get to the park circuit.
Hope that makes any sense….LOL
