This is a resistor board, the outside smaller resistors are the warming resistors which allows a small amount of current to flow thru the bulbs to make them light quicker like a flash. When using leds this small current is enough to light the bulb when they should be off. As others have said the resistors can be removed or the black wire on the board can be removed.

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Yes!

Your fine since you removed the ground wires. LEDs can flicker from voltage spikes. Most of the time the spikes are caused by open diodes on coils. When a coil fires a magnetic field collapses causing a high voltage spike, the diode shunts the spike to ground. If the spike isn't shunted to ground it can pulse different transistors in the game, since LEDs need very little power to work they may flicker.

Nothing to do with the resistors. If you think the flicker happens when flipping, then replace the diodes on the flipper coils.

Sorry for not seeing this sooner.
If you activate the flipper and you see one of the leds flicker then yes replace that flipper coil's diodes. Here is a pic of the correct stock coil for a Pinbot. It has a single diode across the outer lugs of the coil. The diode must be installed in the correct direction. The silver band faces the power wire.
Lastly when the diode ages it will usually go open from the high voltage spikes that come from the coil when de-energized and magnetic field collapses. The diode shunts this high voltage to ground so it wont cause any problems. If the diode opens the high voltage will travel back to the power supply and then to all the boards. This can cause damage to sensitive electronic components.
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When in doubt, replace it. 7 cents each wont break the bank.

Playball!!!