The way that mechanism works is thus:
There is an extension on what's called the arm lever underneath the base plate. This is attached to the lower end of the tonearm and swings with it.
This extension, when the arm gets near the center of the record, pushes on a trip lever attached to the big red cycle cam.
The trip lever moves the trip pawl via the little white donut. The donut is mounted on the pawl in a kind of groove and rests against the trip lever. Thus, there is friction between the two parts and the pawl moves when the lever moves.
As long as the arm progression is slow, like when in the recorded groove section of the record, the pawl gets pushed back out of the way by the stud on the platter spindle. This is also why the white donut is there so the two parts can move separately. The trip lever needs to stay in the same place while the pawl is pushed back by the stud.
This is called a velocity trip mechanism, by the way.
When the stylus/arm moves quickly as in the lead out grooves, the pawl moves into the way of the stud on the platter spindle and gets pushed to turn the big red cam until the gear teeth engage and the cycle starts.
The donut should fit tight enough in the groove on the pawl so it doesn't easily turn. If it seems to turn too easily, I suppose a very small amount of superglue could be used to attach it to the pawl. It doesn't need to move in the groove. Just against the lever surface.
I hope this is clear.