Manchester,
Like ghost mentioned, this could to be a work timer / wrap up timer. That being said, in Contact Center Client, you should see that Agent appear on "Work timer" (see attached screenshot).
System Idle, however, would be if the agent is Idle, but not present in any Agent Groups that he's a member of. This could explain the reason why you are seeing the agent sitting Idle while there are calls in queue.
What version of CCM are you running? Are you using Agent Group Presence?
Cheers,
Kevin M.
prairieFyre Software Inc.