Normally, one just leaves tmux running, but in one situation I need it to go away when I am no longer actively using it.

If I have a tmux session with some windows open, I can have it killed automatically if I log out from the shell or manually close my terminal window by using 'destroy-unattached'.

That covers manual shell. However, if the SSH session goes away on its own, say by just closing a laptop lid and leaving it alone, then the session remains. Or if I use ~. to close the SSH connection, the session remains, too. Maybe some specific signals need to be trapped by the shell to call a script to finish off the left over sessions?

What is a reliable way to have tmux close its sessions for that account when the SSH connection timesout?

did you try to auto logout (of shell) using the variable TMOUT?

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Thanks. I think TMOUT might be an answer.

Further tests in place take more time.