Both of the longer arms driven by the solenoid plungers have shorter arms that engage the gear teeth. Each one should fall into the gap between teeth as its longer arm activates. The one on the advance arm falls into the gap and pushes the tooth forward. The one on the subtract arm falls into the gap to keep the gear from rewinding more than one step.
If that's not working reliably it could be that the shorter arms are worn (so they drop into the gap but work their way out), or that they're not swinging freely on their pivots (so they don't drop into the gap completely). If they're not swinging freely the shoulder bolt could be too tight or they could be bound up with dirt, grease and grime. A little dental floss and your favorite cleaner might help clean that out.
If you do remove the arms, be careful with the shoulder bolts. They're notorious for shearing right off. You'll have better luck removing the nut and lock washer from the back of the frame first before trying to back out the shoulder bolt.
For those unfamiliar, the video at https://www.funwithpinball.com/exhibits/small-boards#CreditUnit shows a closeup of this unit in action at about 0:36.