It sounds like your player unit is having some trouble either stepping cleanly, or some of the switches in it aren't changing states as they should. If you remove the screw in the upper right corner that holds the player unit in place, it will drop down 90 degrees or so. From that position, you should be able to see all the switches clearly. Take a good light and get in there carefully and clean the contacts. After you've cleaned them, make the unit step around and watch each of the switches to see that it's opening and closing as it should. When they're all opening and closing correctly, look at the back side of the switches and make sure there aren't any tabs or wires touching or disconnected. It's really important to be careful and thorough when doing this.

When you're done with that, screw the player unit back into it's normal upright position and work the plunger with your finger to watch it step around. Does it move quickly to each new position? Are the rivets and snowshoe contacts clean?

I realize this is kind of a holistic way to approach your problem, but if you can do all that carefully, it may fix your problem and help you avoid some future problems in that area. If it doesn't fix things, at least you know the switches and stepping is working as it should, and you can look elsewhere. But it does sound like your player unit could be the problem.

Make sure those player 1 score reel switches are making good contact as well, opening and closing correctly.

Yes, it looks like there's a switch on the player unit P1E that has to be closed for a pulse from the L relay to get through to the score reel.

With the game set for player 1, press the L relay armature with your finger. Does the 1000 pt score reel move? If so, does the 1000 score reel move when you score 100 pts at a time (tap the M relay armature) and go to the next thousand?

Is the thousands chime ringing?

surfer player unit problem (resized).JPG

Well, if the L relay is moving the 1000 score reel, then the P1E switch is working - the signal is getting through both that switch and the switch on the L relay that is in series with P1E.

There's some disconnect between the 100's score reel and the L relay. There are only 3 switches that fire the L relay when the 100's reel is on 9 and gets a signal to go to zero. You've shown with pressing the L relay manually that the 1000's reel moves, which means that the switch marked "L" in series with P1E on the snippet in post 4 is closing. (I would assume the 1000's chime is working then.) That whole part of the circuit must be working. So it's got to be something in the snippet below, which has to do with the switches on 100's score reel or their wiring.

Just as an overall explanation, the snippet below is how the 1000's reel gets a signal to fire when the 100's reel goes from 9 to 0. You can see the M (100 pt) relay on the right side of the highlighted circuit. When the 100's reel gets to 9, the "9th. pos. 1st. hundreds" switch should close. On the next 100 pt pulse, when the 100's score reel moves, the M switch and "on add 1st. hundreds" switch should both close, completing the electrical connection to the L relay on the far left and energizing it. That should close the L switch on the far right in the snippet on post 4 and complete a circuit through P1E to the 1000's score reel solenoid to advance the reel. Those player unit switches (P1E, P2E, etc.) just route the signal to the proper player's reel...the rest of the circuit is common to all players.
So you showed me that the signal from the L relay is being routed correctly to player 1 - but when the 100's reel goes from 9 to 0, the L relay is not being energized as it should. So it's something in the snippet below.

I apologize, I only have the Surf Champ (4-player) schematic, so that's what I'm posting - yours should be a bit simpler, but similar enough.

Surfer problem (resized).JPG

Glad you got it taken care of. Surfer's a great game!