How to detect SSH timeout with SSHJ SshClient

Question

I'm seeing a situation where an SshClient (fromthe SSHJ library) is connected and then left idle long enough that the SSH connection times out ("timed out waiting for input: auto-logout". I want to gracefully trigger some behavior when this timeout happens, but cannot find any way to programmatically detect it. I would have assumed the Transport's disconnectListener would handle this, but none of the code I put in there is executed by the timeout. Is there some listener or hook somewhere that I can use to tell when my connection has timed out?