That is the EOS switch for the score reel. You say your 10's reel is faulty. When that player (#1? #2?) hits a 10 point switch (e.g. slingshot) your 10 point relay (N) should energize *and stay energized* until the player's score reel tells the N relay it has finished scoring the 10 pts. The circled switch is how the score reel communicates that feedback. The yellow marking below shows the lock-in path for N relay which will stay locked in until ON ADD 1ST. "TENS" opens or ON ADD 2ND. "TENS" opens, depending on the active player.
However, since your switch allegedly is broken/never closing, then the N relay will never "lock in". Meaning it will energize only as long as your playfield switch (e.g. slingshot) is closed. That may not be enough time to mechanically score 10 pts, although your score reel may twitch in trying. If you held a 10 point switch (e.g. behind a rubber) closed, the score reel would fire and then would release when you let go of the playfield switch. By the way, the score reel advances when it's coil releases, not upon its firing.
The other player would not be affected by this.
