8 hours is actually pretty long. we'd say increments from thirty minutes up to a few hours. If someone's as much trouble as to be making a mess in the chat after a several-hour break, then they're something the regular mods probably have to deal with too.

The chat mods should not be selected on a whim. They should be reliable enough to be trusted with full power though. If they abuse power, they should lose it, just as would be the case for moderators. The power to indefinitely mute someone is something that only one or two members of the staff needs. The decision to do that should after all sit deeply enough for people to wait up to a day or two for it to be used, depending on the schedule of those people.