Flippers twitching is almost a surefire indication of dirty optos. Clean those up first and them report back on the problem.

The next thing I would check would be the end of stroke switches. B/W coils have both high power (flip) and low power (hold) windings. When it hits the end of stroke, power switches to the low voltage winding to hold the flipper up. This way you don't burn up the coil. If you're not activating the EOS switch, you may be staying on the high power winding and blowing fuses to protect the coils from melting. This might explain why the coils are buzzing.

Long winded, but that's what I would suggest. Clean optos then check EOS in switch test mode.

I'd check to make sure the connectors on the opto boards are good, then I'd reseat all the connectors and/or ribbon cables on the fliptronics board in the backbox and see it that helps

Definitely keep us posted. Do reseat all the connectors first, though. A lot of times all it takes is that as the pins can develop a patina on them over time which weakens the electrical connection or sometimes just become loose. Especially if the game was moved recently

put the machine in switch edge test and move the flippers to the up position by hand. do the EOS switches test ok?

Yeah. If you're getting intermittent power to the optos, I'd first look at the connectors which have the 12V in and out to the optos. Should be J904 and 905 on the board. Then, I'd start tracing the wires underneath