I found a partial movement for reference. That lever that the stem presses when pushed all the way in (wind position) is the setting lever which presses against a pin that extends through the plate from the dial side. This pin is part of the piece (vibrating arm) that your cam spring (the one that releases when removed from case) presses against (note: nomenclature taken from Swigarts Illustrated Manual of American Watch Movements). When the stem is in its normal winding position the setting mech. will be disengaged. This part appears to be working well when you manually activate things according to your description.
The setting lever shouldn’t be free wheeling as it needs to engage and disengage the winding/setting function. If the pin is there but things seem to flop back and forth on the dial side then you may have a missing or broken spring somewhere or something may not be seated all the way down or in it’s intended position.
The shipper and shipper spring I spoke of is just another name for clutch lever and spring. You may also hear it referred to by other names like “sliding lever” “sliding lever spring” etc.
I don’t know of any diagram but will search around for one for you. Also if it will help then feel free to take a couple of pics. and I will put some arrows pointing to the different parts and will try to explain how the mech. operates. I would take a pic of my partial movement but my camera is still putting out blurry close up shots so it probably wouldn’t be too clear.
One of the videos in the online course covers a lever set mechanism which is “similar” which might be of help. It’s at “Watch Video #3 part 1” and then click on “Lever Set 2 -415” in the quick navigation menu in the controller.
I hope this helps but I know that trying to decipher my descriptions and explanations can be “challenging” at times so please let us know and also post some pics if it will help.
Good luck BYJWR1,