There are several places in the linkage from the pedal to the starter where pivot holes wear oblong and/or the ends of linkages wear down to smaller diameters. Add up a few wear points, and you run out of movement to the point that the starter drive engages the flywheel, but the button doesn't get pushed far enough to spin the motor. Inspect the link from the pedal linkage to the starter lever for wear, and also take a look at the two loops where the pedal linkage bolts to the bell housing. Over a few decades of use and untold thousands of starts, things can get pretty sloppy.
The strap from the engine to the frame is currently supplying a ground path for the lights, horn, and other body-mounted electrical items. I'd suggest disconnecting that junction and wire-brushing everything shiny clean. All it takes is one dirty or loose connection anywhere to interrupt the circuit or make it intermittent.
Jerry
