Decades of starts will wear all the pivot points where the linkage moves. You'll need to disassemble things and look for wear grooves, oblong holes, etc. Weld, fabricate bushings, or do whatever it takes to get the linkage moving everything like it did back in the dark ages.
It's also possible that there's a "dead spot" on the starter armature that creates an open circuit when it stops in the wrong place, or worn brushes that aren't seating properly on the armature. Try a few gentle taps with a medium-sized ball peen hammer to the back end of the starter housing and try the pedal again.
Jerry
