Welcome to Pinside. Once the Score Reels have all reset to zero and the Ball Count has counted down to zero, the Ball Count should count up to 5 (or 3 if you game is set that way) and send a ball to the shooter lane. For the Ball Count to count up the W/Add Ball Count Unit relay needs to fire through the circuit in red:
Gold Strike W relay (resized).jpg
As you can see a number of switches need to close to fire the W relay. Rather than checking them all, start by making some observations. First, does the W relay ever fire? (If it does the problem is downstream from this relay and not shown in this schematic.) Next does the V/1st Ball relay ever fire? How about the Z/Reset relay?

If the V relay fires you know that the four switches across the top of the schematic in the Score Reels are working. That leaves just three other switches to check.

If you change your game back and forth from a 3 ball game to a 5 ball game (with a small jones plug in one of two available sockets) and the problem is the same chances are that the two Score Motor switches aren't the problem (since both would need to be bad).

That would leave a switch on the Z relay and another on the Ball Count unit. The Ball Count Zero position switch is likely closed by a peg on the Ball Count Unit gear. You can see how that works in the video at https://www.funwithpinball.com/exhibits/small-boards#BallCountUnit. The video shows a Williams Ball Count Unit but yours will be very similar.

Before you start cleaning or adjusting anything though I'd read up on such things because unless you're familiar it just as easy to introduce new problems as it is to fix the existing problem.

/Mark