Did you make any progress? Until a more expert pinsider chimes in, I can try to help.
It looks like the player unit it is advancing from ball 1-5 ok (I'd ignore the intermittent/non-working ball# lights for now). It seems to get fouled up at the last ball or game over stage(s). After you drain ball 5 and collect bonus, it is kicking another ball to shooter lane, advancing the player unit past ball 5, then starting to reset several score reels as part of a new game reset sequence. Then when this ball is played, it is finishing the reset of the score reels for the new game.
I'd see if the last ball relay XB does anything when you drain ball 4. Get to ball 4, then lift playfield and simulate a drain by holding closed the outhole switch from underneath - be ready for the kicker to kick ball 5 to shooter, so watch your fingers. As you do this, watch for activity from the XB relay (among the relays in the control bank with the big reset bar on the bottom of the cab).
I'd do the same when you drain ball 5, but observe for activity from the game over relay QB (also in the control bank).
Any other ideas?