Sometimes people just need a good sanity check.
So, my flashers are fixed, and the problem was several freak coincidences stacked on top of what I saw as a very unlikely problem.
All the flashers are daisy chained by one wire (RED/WHT), and I made an important assumption that is true in 99% of cases. I assumed that a set of sockets connected by a wire with good solder joints will, in fact, carry current. I was not expecting a solidly connected wire to apparently have an internal break. The wire running between the left ramp flasher and the rear flashers (a connector that branches off to the others as well) was defective.
"But wait," you might say as you think about this wiring configuration. "If that's the wire that was secretly broken, then why didn't the ramp flasher still work?"
Because the ramp flasher DID work.
I was right when I said that the bulbs and sockets were in good shape; they are all fine and work great. But to check a bulb, I pulled the dome off the Blast Zone flasher and tested it, both visually and with my meter. Nothing wrong with this. However, there is only one flasher on Road Show on which the wire lugs are conveniently exposed for testing, and that's the left ramp flasher. So I tested that one for voltage, and all was fine.
So why didn't that one flasher work, which would have clued me in that there was a connection problem and helped me solve the issue long ago?
BECAUSE THAT ONE BULB WAS MISSING.
It never occurred to me that my flasher circuit could be perfect except that the first bulb was removed and the wire was broken internally after that. The only explanation I can possibly think of is that the game had one working flasher, but that one flasher was disabled to avoid calling attention to the fact that the game had only one working flasher. Last person to work on the machine apparently never thought to check for a wire that wouldn't conduct.
Thanks guys! I would still be in the dark (literally) if I hadn't been pushed to scrutinize the bulbs a little harder.
Edit: Just to clarify for those not familiar with this game, most of this game's flasher bulbs are not directly visible, as they are hidden inside the lenses of the flasher domes. You cannot really tell if a bulb is missing unless you specifically remove the dome.