Thanks for the post (and great Fonze reference!).

The problem that comes to mind for me is that the Output Shaft (#50 in the attached diagram) isn't mating to the #46 Gear & Pin Assy correctly.
The Output Shaft has a slotted cutout that fits on top of the pin on the #46 Gear Assy.. It may have popped off, and you won't get any reciprocating motion of this is the case.

Also check the teeth on the #46 Gear & Pin Assy, as they may be worn, which won't allow it to mate with the Armature gear teeth.
I would say the problem lies there, if the motor obviously turns but you don't have any reciprocation.

Hope this helps, feel free to reply with anything else.

- MTR