Unless you can post a schematic for your game we'll have to use one for Deluxe Pinch Hitter from IPDB.org which might be similar:
Deluxe Pinch Hitter Hi Score Impulse relay (resized).jpg
I think the Hi Score Impulse relay (bottom right in red) should fire on this game to advance the high score score reels. For that to happen a path needs to be completed through one switch on the Run Unit and through the three step switches in red.

At the top of the schematic the Hi Score 10 point score reel disc has four positions. Position 1 does nothing. Position 2 (20+ runs) selects a set of 10 contacts on the Run Unit disc. Position 3 (30+ runs) selects the next 10 contacts, etc.

The Run Unit disc has 10 pairs contacts wired together. So for example the contact for 21 runs is wired to the contact for 31 runs, and it's the Hi Score 10 point score reel above that selects between the two.

Below that the Hi Score 1 run score reel selects one of the 10 pairs of contacts from the Run Unit disc.

So for example if the High Score reels show 20 runs and the player has scored 20 runs the path in red should be complete. When a run is scored the Run Unit switch should close which should fire the High Score Impulse relay which should advance the High Score 1 runs score reel.

If you're lucky the Run Unit switch needs to be cleaned or adjusted. If not you'll need to trace through the three steppers.

/Mark

It might be between 3rd base and home plate on the Man Running Unit.

How does your schematic compare to the one I posted earlier? From the small piece you show it looks about the same.

Next questions to answer include:
- Are you checking the right EOS switch? Do the colors on the schematic match the colors of the switch you checked?
- Can the EOS switch actually conduct electricity when it's closed? If the contacts are dirty it won't matter if it's open or closed. Use a meter to see if there's an electrical path through the switch when it's closed.
- Is there a path through each of the other three units? If the High Score reels show 20 and the Runs Scored show 20 for example, there should be almost no resistance along the path highlighted in red, from the EOS switch to the power rail on the left side of the schematic. In other words there should be almost no resistance from the 78-1 wire trhough the 62-1 wire and the 54 wire to the common (yellow?) power rail wire. There should be a key on your schematic to tell you what colors the numbers represent.

There's rarely information available about where to find switches in a game.

What switches are you looking for? There's only one switch in the path highlighted in reply #2. The rest of the path goes through step units or score reels which drag a wiper across a series of contacts on a board as it rotates. On the schematic each box made of dashed lines is a step unit or score reel and the circles inside the boxes represent the contacts on that unit. A wiper should only touch one contact at a time so each step would complete a different path through a different contact.

You need to work your way through the stepper and score reels because that's likely where the problem is. Somewhere a wiper is probably not making good contact with a contact or a wire has come loose.

Start with the simplest one, the 10s digit high score reel at the top of the schematic in reply #2 labeled "Hi Score 10 D.U. Disc". The unlabeled wire that comes in from the top left corner is yellow (or 30) and comes in from the transformer. When the score reel shows 1 (for 10 runs) there should be no path through the score reel. When it shows 2 (for 20 runs) there should be a low resistance electrical path from the 30/yellow wire to the 54/white-green wire (highlighted in red). All of the wires are probably soldered to the side of the score reel. Use your meter to convince yourself that there is little to no resistance between 30/yellow and 54/green-white when the score reel shows a 2. Then step to 30 runs and see if yellow connects to the 57/white-orange wire and then step to 40 runs and see if 30/yellow connects to 59/white-grey.

Once you can see the path through this score reel open and close and understand what's going on, try the experiment in reply #9.

If talking through it might help more consider this: https://pinside.com/pinball/forum/topic/an-em-pinball-online-repair-clinic