Reporting is the way forward; the Agent performance report will show if the call has been returned to queue from time out or otherwise.
If you look at the last two columns, the last will be Return to queue from timeout i.e. call has rang out on agent phone, & has returned to queue as it was unanswered. The second last column should tell you all the other calls returned to queue for other reasons, e.g. agent going on not ready, agent going on DN call, etc...
If he is doing the "Not Ready" trick i.e. hitting "Not Ready" really quickly & then immediately going back into a ready state, this will reset his idle call time back to zero so he will no longer be the longest idle agent & will not receive the next call.
As far as I know, if he is doing this, his status will not show as Not Ready in the Agent login/logout report unless he is Not Ready for a time period longer than the few miliseconds it takes him to hit that key twice ~ so the only way of seeing the bounced calls is by checking the second last column in the agent performance report & see if he has any of these calls returned to queue.
Return Calls
From
To Time
Que Out