Sounds like the breaker inside the switch is doing its job.
Make sure the switch has a good ground (tighten the switch screws, if needed)
@CBODY67 has some good info. Motor, wiring, bulkhead connections.
I agree. I see on feeBay guys selling JUST THE BOX! I'm pretty sure an "NOS" switch is going into it.
And "Time Waster" (AKA Facebook) has gotten to be a scammers mecca, with little to no oversight.
The black wire is power in (probably from the plastic push button switch).
Black to brown is low
Black to green is high
I have a 2587564, NOS MoPar, if you are still looking.
Do you have 2 or 3 speed wipers? A pic of the wiper motor will tell us.
And am I to understand that when you flip the switch to "off" the wiper arms park but don't go down enough? Have they ever gone down all the way since owning the car?
Back when I was a Californian I did quite a bit of "testing" by getting 2 gaskets and putting a metal shim between them. There was even a factory block off plate for use on 49 state applications. This was when we had to pass a visual test by the CHP at roadside inspections.
You might have to...
If you were to ground the feed wire at the sender, turn the key to 'on', does the dash gauge go to full? I used to use a remote starter push button for this as my shop was a one man show.
I rebuild 4-5 of this type per month. You do need to get it apart (the rivets) to get at the corrosion that is between the contact (green corrosion) and the rheostat (spring)
1969 Imperial had 2 different style dimmers.
This style I rebuild
This style I do not
You might want to at least feel up behind it to see if it is even plugged in.
There is a circuit breaker inside the variable switch that will open / close due to heat (too much of a draw somewhere).
I have rebuilt easily hundreds of this type(A,C and E and Imperial have the same internals).
If you have a factory shop manual it will explain how to test the motor...
Would this duplicate the symptoms?
Battery charger hooked up, engine OFF
Key on ACCY
Heater ON
Fan on HIGH
Sit down, watch a ball game in the garage, wait........