There are two relays that are always energized in your machine when the power switch is on. One is on the coin door. The other one, I think the one you are referring to, is on the motor board on the bottom of the cabinet. It is called the LOCK relay. It is normal for the coil to be warm, but not hot. The coil was likely replaced some time in the past with the wrong coil.

The LOCK relay by the way is not part of the configuration to set up free play.

That's fine. Common in home use for people to disconnect it. You don't need it unless you are collecting coins. Its purpose is to reject coins when the machine is powered off.

The coil for the 2 coin 3 play relay should be a G-32-2500 and it should not be energized all the time. First check the coin chutes for stuck or misadjusted switch. Common for those switch triggers to get mangled. Check the switch at score motor 3F, the ball index relay, and the 2 coin 3 play relay itself for proper operation. Also check the 2 coin chute relay. Maybe the 2 coin 3 play adjustable jones plug is somehow plugged into a wrong receptacle.

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Glad I could help. Send me the link to your other thread and I'll chime in if I can help there too.