Currently we have an idle_timeout= keyword. It's great! It stops people from leaving clusters on, potentially racking up needless cloud expenses.

I sometimes find myself wanting a different timeout when all clients have gone. For example I might want a one-hour timeout if I'm connected from my Jupyter session, but once I've disconnected I probably only want a five minute timeout (long enough for me to hit refresh on my notebook and reconnect).

With this in mind I'll propose a idle_timeout_no_clients= keyword and config value (better names welcome) that would, presumably, be set more aggressively.

cc @fjetter @jrbourbeau (maybe useful for coiled.run) and @ntabris (because I think he cares about these things).