We failed to blow the fuse using all the switches available. One by one we tried them all since that would be the easiest way to find the problem. No luck.
Figuring (hoping) it was probably some obvious fault, we then removed the front plastics to take a look.
We disconnected and reconnected everything just for fun as we inspected all the wires, looking for anything unusual. A couple of minutes into it, we found some tape-wrapped wires that weren't original. Unwrapping the wires, we found
Why the hand brake switch would cause the problem is beyond me, but somebody replaced the connectors and wrapped them tightly together either causing or trying to fix the obvious short circuit evidenced by the melted plastic. Separate wrapping is better.
So we buttoned it up since we couldn't find anything else, fixing and improving the little things along the way. The cylindrical fuse was replaced with a modern bladed fuse holder and placed for easy access. The positive battery connector was not original and too flexy for my liking so we replaced that too, testing the bike at every step along the way.
The test rides were fine. We bled the front brakes and adjusted the rear. Now I'll lead him on some longer runs to see if he can learn some of the main routes and eventually go out by himself.