This is somewhat possible with the introduction of the hook function in tmux 2.2 and 2.3 ( tmux changelog )
You should be able to start the clock that appears after the window has quieted down for a certain period of time. Monitoring user inactivity is still not possible.
You can set the window option monitor-silenceand use the hook alert-silenceto start the clock.
See the tmux 2.3 man page for hooks and silence on the monitor.
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