How can I set up my Mumble server to automatically send people to the AFK channel after they have been inactive for X minutes?
This post probably does belong on server fault rather than on superuser. Even if you feel like an end user, you're still running a server application that clients are connecting to.
That being said, the solution to the problem is to utilize MuMo (Mumble Moderator), which allows Python scripting to interact with the Mumble server, reducing the expertise requirement for simple server moderation to a minimum.
The latest version also includes a script for automatically shoving AFK users into a specified "idling" channel.