Given free rein, I’d absolutely love to tell people that needing me to show them how to do X in Excel is actually not a vacation-interrupting emergency and there are tons of free videos that would explain that, if they did not want to contact the actual departments who handle tech support and training. Or that this project they’ve known about for a month but decided to keep under their hat until it became an emergency is something they’ll need to resolve themselves. But that would not fly at all.
Having easy access to your work even when you away from the office doesn’t mean you don’t take time to disconnect and relax for a while. You deserve to take a break, muting all the mailboxes and switching off your work phone for a couple of days or weeks. However, there is a lot you should put in place before going away from your office, in the true sense.

Anything worded like Option 1 would never fly at my workplace, exactly because of this. I have colleagues who complain to upper management if their non-urgent tech support questions (that a whole troubleshooting website already answers) don’t get an answer from me or my boss within half a day. And oh, did I mention our job is not actually tech support?
Well, but as others have pointed out, that depends on the part-time job and the industry. If you don’t work Tuesdays and Thursdays, but those are considered standard hours in your business, clients or other folks outside the office might email you on Tuesday morning with something important, not hear back and not know why — and get irritated. If they get an OOO, they now know what to expect or they have a backup option if the matter is urgent.