Well, the problem is back. The bike just refused to start when I was out getting lunch one day. I pulled out the battery and walked it home to recharge it, but it turned out to be mostly charged. When I returned the battery to the bike, the bike started just fine.
Then the next day, the bike started, but the instruments were resetting with their power-on sweep continuously. So, I aborted that trip and returned home. Good thing, too, since the bike wouldn't start again. Now the instrument backlights come on, but the LCD display doesn't show anything. The headlights and fuel pump come on, and I see the neutral light dim when I thumb the starter (no relay click, though).
So, I'm thinking a short-to-ground somewhere again. This time, I'll leave the key in the ignition when I pull apart the bike, and see if messing with the wires gives me a clue about where the short could be.