OK, Update after doing some investigation on the Flip-Flop machine...
Everything looks to be operating properly on the score motor and on the bonus unit. Looking at other relays, the bonus score coil is releasing when the bonus cadence is delayed then will energize and bonus will continue. That coil looks to be in good shape. Looking at what controls that coil, the bonus zero coil appears to be very burned. I have noticed a very loud buzz when playing that doesn't appear until second ball and verified that this coil is the one making the noise, you can feel it when you touch it and if you gently knock on it you can change the intensity of the buzzing. It is actuating its switches but I think it is weak and maybe not holding the switches together strong enough. If I run the end of ball bonus while holding this coil in the energized position, it fixes the problem. If I run it again without holding it, the problem comes back. If you check resistance, this coil is supposed to be 78 ohms, I am getting less than 10. I am next going to look at all of the switches on this relay and see if an adjustment helps at all and then plan to replace the coil (which I plan to do regardless if the switch adjustment helps). While checking other coils for sanity of the low reading I was getting on the bonus zero, I also found my lock coil is also burned up looking and at sub-10 ohms versus its 105 ohm rating so I will be replacing that one as well.
fb-rider, unless the thrill of the chase is calling you, you may want to take a look at your bonus zero coil on Captain Fantastic. I just held the switches in the energized position by holding a piece of wood against the plastic piece that actuates the switches when the coil is energized to fix the issue showing an issue with this coil and or switches.