Well, I owe y'all a close-out on this one.
Weekend back I took the clutch switch off, gave it a visual inspection (that is, I pushed the little button to see that it worked), made sure it was clean, and then put it back on. Since then, the bike has started perfectly. So I'm going to say that is a job done!
The switch is the simplest of things, not sure how it could ever go bad, other than just WEAR OUT. It's nothing but a spring and two contacts, so there's nothing in there to go bad (like a circuit board).