Hey GlideFather! Nice nickname!

So to answer your first question, I was hoping not to have my Service Desk Agents have to remember to set themselves Offline before closing their browser. That sounds like an extra step that shouldn't need to be there.

One thing I thought I'd try is on the AWA Assignment Rule Rejection Handling section, to set up a relatively short Timeout and have the Agent's state move to Away so that if they're served a chat and don't Accept / Reject it, they won't get any more. This will cause our customers to incur additional wait time from time to time though, so I'd love to see if there's another way.