I can't say new Game Moderator command but more likely modified.
/admin_mute <length> <username> is the original command to mute a specific player in-game.
My suggestion;
Modify it to /admin_mute <length> | <username> | <reason>
Whenever someone is spamming or breaking the rules, the Game Moderators can just use the command to mute the player for instance;
/admin_mute 5m (yes, minutes, not hours - you should also add minutes option for the command) | iLikeSpamming | Constantly spamming lobby chat.
So whenever one of the GM's use the command, on the other side of the computer, in our case is the user "iLikeSpamming" - should pop up a green message telling him for example;
"Your chat has been blocked for 5 minutes - <here the reason should show, the one the Game Moderator entered as a reason and in our case that would be> constantly spamming lobby chat."
Much more reliable instead of going to the Administrator Panel to mute the player and disconnect him so the mute can apply on his account.