Timeout When Not Connected

[texmachina]

Following on the timeout thread, I see the ability to use the timeout-minutes directive that GHA accepts, which works mostly fine. However, the action we are looking to achieve is to use timeout in a bit of a different manner where tmate times out in X minutes if no one connects. If someone does connect, we want the session to remain live until they exit as normal (or perhaps have an additional Y timeout as a time limit even if a connection is open).

Is this possible currently in some form of config?