It shouldn't unless you are inserting coins or the game is advancing to the next player. Your schematic would clue you into what other contacts control the lockout coil.

The coin lockout coils are irritating on most games. I typically disconnect the single wire to that coil and tape it up as that keeps it from buzzing and getting hot. Even if you decide to run coins through it, I never find the coil that useful. But if you decide to reconnect it, it's easy enough to do.

The Coin Lockout will drop out shortly after the Score Motor starts turning (when the Motor 1C switch opens) and stay idle until the the Motor 1C switch closes again at the end of the cycle:
Lawman Coin Lockout (resized).jpg
The game can't do more than one thing at a time if the Score Motor is involved. So if the Score Motor is running (adding 500 points for example) other things that require it are either ignored (like hitting a 2nd 500 point target) or disabled (like the Coin Lockout is) until the Score Motor stops.

/Mark

The coin lockout will drop out when the score motor runs. That is the design of that circuit. It is supposed to do that. It prevents inserting a coin when the motor runs in an effort to get extra credits.