One hour. You can do it on a lunch break.
Leave a toon parked in a Day Job location every end-of-session for about a week; as you note, it has to be logged off.
Excuse me, my eyes just rolled away. Right back. (Not your suggestion, just that there might be players who think this way.)
This alt is apparently known for doing this, on a continual basis. There are vague allusions to SG promotion and recruiting above, but the game has a perfectly serviceable (if clumsy) email system for that, and also noted above is that this instance seems to be completely inert.
Not sure any 50+ could just Rest and walk away for days without noticing the game is still active. And others suggest there are deliberate reasons for doing this, hence again my question: What's the point?