Flashers are run by Transistors you can locate those Transistors in the manual and test them with a multimeter.It sounds like the flasher or flashers have locked on due to shorted Transistors.

Do they flash REALLY REALLY bright? That could indicate that they're getting 50v instead of 20v - I can't think of any plausible way for that to come about accidentally without trashing lots of other stuff - but at the same times, I can't think of any other explanation for flashers blowing that fast. Check the voltage on the bulbs (remember that you need to hold down the coin door switch to do this) - power supply should be +20v (give or take a few volts).

If it's getting the correct voltage... I don't know what to say..... I'd start to suspect crap bulbs, honestly. If it's got 20v on it, since there's no vaguely plausible way for the transistor to pull to below ground, then it's getting 20v put across it, and it should be behaving like flashers normally do. The bulbs are only rated at 13v (for automotive use), but pins drive them with 20v to get a decent flash.

Also, I assume you've confirmed that the bulbs really are burned out, and its not just a flakey socket that only works when you've just poked it?

Don't measure the voltage across the bulb while it's flashing. You know one side is going to be grounded, when it's on, so you can use any ground you want to measure the voltage it's getting. (flashers and coils always have the +50v or +20v on them, and are fired by grounding the other wire)

Measure between ground (the grounding strap stapled to the inside of the cabinet is the easiest way to get on ground) and the power side of the flasher.

You win! Thanks for posting the solution...