I would start with something simple like checking the linkage for binding. After that I'd move to electrical connections - EOS switch, loose wires, caps, diodes, broken coil winding wires at the lugs.

Also with this type of flipper hang up it is a great idea to turn off the machine when it hangs.
If the flipper falls on its own accord it is likely electrical.
If the flipper stays in the up position or where it started sticking then it is likely mechanical.

I would check linkage and assembly for binding as Wolf mentioned. Also if the height of the flipper through the bushing is wrong or slips it can (drag) which will seem like a physical bind. Same is true for linkage it needs to line up just right or you will have extra tension when you do not need any.

The "high power winding" of the coil sounds like it's open or barely making a connection. Get a very close look at where the very small coil wires are soldered to the lugs. Tug on each slightly to confirm a solid grip. Also, check the two windings with the ohm setting on a voltmeter.

Modern flipper coils have a "low" 6V winding, and a "high" 40-60V winding. Hence, the soldering "3 lugs".

You have two switches on each flipper assembly one is the EOS and the other is Coil High power you need to adjust the coil switch, the contacts sounds like they are getting flaky.

What about the cabinet switches? Are they leaf switches or micro switches?

I know this sounds stupidly simple but I had a similar thing with my JP. It was driving me mad because when I lift the PF to observe it everything was totally fine.

Turns out I had put the shooter lane coil back in rotated 90º from normal and so the wires were interfering with the flipper leaf switch.

So check for something physically affecting the way of the flipper mech or switch/button. Sounds like your issue is odd enough to be a physical problem and not electrical.