More thoughts from an aging brain!
My first SQ-A body developed a hang-up in the shutter release; initially the button would work, but not a cable release. After tormenting myself further it seemed to get worse. I recall that with the back off and multi-exposure on, I could prod a link up near the lens mount and at least coax something to work. This was around the time I was attempting to use the body with a pinhole body cap and no lens.
I believe the link is related to the coupling to the cocking pins on the lens, and protrudes more to the right under some states of operation. The link appears just to the left of the wooden skewer here:
(Excuse the dust!)
In this view, on the right (next to the silly skewer) is a bifurcated tab that appears to transfer motion from winding the crank to cock the lens. (The view disappears as the mirror descends!)
Also on that lower right, at the back mounting surface, is a hole with a pin in the center that works magic in interlocking film winding. I would be tempted to gently poke each of those items a bit and see if anything changes. (The views are as seen from the back with ground glass up, crank on right.)
Some day I hope to take my screwed up (camera!) body apart and learn what's in there, but I'm afraid I don't see it in my near future.