One possible way to test the winding mechanism without pulling it apart, is to whack an MD4 motor drive on and run a roll through. There are multi function backs for the F3, specifically the MF-18, which are only to be operated with a drive attached. The reason supplied is to ensure even spacing between frames. Which is important as this back imprints either the date or numbers between the frames, therefore the frame spacing needs to be wide and accurate.
You could then see if the winder mechanism is dodgy; maybe.
$70 AUD is pretty good, or the camera may be pretty stuffed; but still work (mostly).
Mick.