Does the high score advance if you manually close the Hi Score Imp relay? If so you know the problem is getting the signal to that relay, and not in getting the signal from that relay to the High Score reels.
If the High Score Reel advances when you close the relay, it might be the Run Unit EOS switch (orange-black to white-blue wires) at the top of your schematic photo. If not we'd need to see the rest of the circuit for the High Score Imp relay.
/Mark