Maybe if you hot wired the engine to start you could eliminate some of the variables.
Please tell me if I'm wrong.

This might not work on a 122 if it has the armoured cable still in place. But generally a jumper is run from the battery positive to the + terminal of the coil-a temporary coil could be fitted to accomplish this and would eliminate more variables, then "short" the battery terminal of the starter to wire on the solenoid (when I was much, much younger this was accomplished with a screwdriver! (lots of sparks, melted threads and generally a low born but exciting alternative to a key). The engine should turn and start. There are much better ways of course. In my early Fords the solenoid was mounted on an inner fender and was equipped with a push button that could be used to turn the engine over from the engine compartment. Any length of wire with a switch in it would act the same.

If the engine still persists on spinning even after you disconnect the coil to battery wire then I'd say the problem lies in the starter. If not the switch or the wiring harness.

Matt's comments are (as usual) very good.
One other possibility might be that the starter contacts in your ignition switch are
fragmenting or sticking, however disconnecting the small wire from the solenoid should
show if that is the problem.
Although a 122 will usually work very well with a surprisingly weak battery, sometimes
they will do some pretty strange stuff! Therefore a good charge is always good.
--
George Downs Bartlesville, Oklahoma

It would be nice if you could get it to happen again...

While it's 'slowly turning over' of its own accord, open the hood and pull the small wire off the solenoid. It should just be a spade clip. (small wire powers solenoid, biggie wire powers starter which, of course, is switched on by the solenoid).

If you pull that wire, does it stop turning over? If so, chase said wire to the ignition switch to make sure it's not making contact with any other 'hot' wires along the way. Most likely places are at the starter (most likely, check for frayed wires, a dropped penny or washer, etc), or at the back of the ignition switch, in that order. (this is the wire that will eventually go to your new starter button)

If it doesn't stop turning over, I'd suspect a sticking solenoid.

I seem to recall having the same issue, when the battery was very low. Why a low battery might cause that, I can't say. Perhaps the starter gets locked into the ring gear on the flywheel, and since the car isn't starting or even firing, the gear stays engaged, therefore, solenoid doesn't kick back, and it keeps providing power to the starter. When the battery is good, the car starts up (or even fires), and there's enough action between the gears that their disengagement is easy. Just a guess, and I'd call that a sticky solenoid anyhow.






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-Matt I ♥ my ♂