I think Data East only used single winding coils. The power to the flippers is controlled by a separate board. The flipper coil gets a timed pulse of high voltage then it switches to a low voltage hold level to avoid burning out the coil.
I am pretty sure the board has some logic in it where it will ignore a permanently closed EOS switch. I think if the EOS is working the board will send through another pulse of high voltage if is see the switch open and close (like if a ball hit the flipper and pushed the flipper backwards)
If bypassing the EOS on this machine left the coil power at high voltage I would assume that the coils would have been burned out long ago. It would not take someone cradling a ball for very long to start to burn up a flipper coil if it was left at high voltage.
Try moving the wires to the correct spots on the EOS switch. Someone was nice enough to not totally remove the switches. See if it makes any difference.
As I recall Data East can have flipper problems if the pins/solder connectors on the flipper control board are marginal. I look at the pins and check for broken solder joints at the pin to board connection and reflow if needed.
Best of luck.