If your Bonus Score relay doesn't fire when the ball drains, check the path in red on the right side:
Hi Deal Bonus Score relay (resized).jpg
If the Bonus Score relay fires but relaxes immediately check the path in black on the left side.

/Mark

If the Bonus Score relay fires it means that the path in red works. The circuit on the left in black is the lock in circuit for the Bonus Score relay. It should hold the Bonus Score Relay on until the bonus has been counted.

Once the Bonus Score relay has fired it should close its own lock in switch in the lock in path. Also in the lock in path is another switch on the Bonus Unit that should be closed until the bonus has counted down to the zero position. Together those two switches when closed should keep the Bonus Score relay active while the bonus counts down.

So if your Bonus Score relay does not stay active until the bonus reaches zero either its own lock in switch is not closing or the Bonus Unit zero position switch isn't closed when there is a bonus to count, or there's a wiring issue in that path.

The Bonus Unit is probably a step unit. If you manually advance it (by pushing the plunger into the step up solenoid and then releasing it) the lights that keep track of the bonus will probably advance too. If you manually reset it (doing the same thing with the other solenoid plunger) you'll eventually reach the zero position where the Zero switch should open.

The lock in switch will be on the Bonus Score relay itself and will have a short jumper wire between the lug of one leaf and the lug of the relay coil.

The schematic also offers wire colors to help verify the switches.

You're looking for a switch that won't close. If the stepper is working grease won't help a switch close.

I don't have the game but the schematic should tell you what you need to know.
Hi Deal Bonus Score relay picture (resized).jpg
On the left is the Bonus Score relay. The wire in the red box goes from the coil solder lug to the lock in switch. It looks like one of the wires on the switch is grey-black which would match the schematic. Is the other wire on that switch white-black as shown on the schematic? That would confirm that that is the lock in switch you're looking for.

On the right is what is presumably the Bonus Unit. When it steps down to zero a pin on the toothed gear should open a normally closed switch - probably the one in the red box. It should have the same white-black wire as the lock in switch on the Bonus Score relay on one side of the switch. The switch next to it that would also activate at zero looks like a Make/Break switch so that's probably not what you're looking for.

If your Bonus Score relay doesn't last through all 15 Bonus Count steps chances are that one or both of those switches isn't closing electrically. Closing visually doesn't count. If you have an alligator clip test lead you could jumper around one switch at a time to see if the circuit starts working. That would tell you whether the switch you bypassed is at fault. Or you could just clean both switches.

I just had a Bally that was having bonus countdown issues. It took a good while to figure it out, but what it ended up being was the bonus unit zero switch. When bonus was at zero, the switch is open. As soon as bonus increases, then the switch closes. The issue was the switch was closed, but just barely. Meaning it looked closed when I examined it with the power off. But as soon as the bonus mechanism fired during the countdown cycle, I believe the mechanical movement caused the switch to open during the cycle. This made the machine logic say bonus was complete. I adjusted that zero switch to have a bit more force to keep the blades closed and the problem was solved. It took me a few hours to go through the whole bonus circuit and verify all the relays and cycles. I was thrilled to figure out the issue.

The point is, check your switch blades and their open gaps and closed force. I'm not saying adjust each one. NO! Look at the schematic and see what correlates and check those switch(es).