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.
If the person keeps you on the message thread in which they then contact someone else (ideally, the person you stated in your out of office message as the one who’s handling urgent issues in your absence), you are literally kept in the loop and can see for yourself that all was handled when you get back. Of course, this works even better if you check the most recent items in your inbox first when you get back.

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After I tweeted this example, dozens of people sent me examples of OOO messages they’d set or particularly good examples they’d seen in the wild. One example from a boss (via a TikTok) who offers emailers a decision tree of sorts. “Option 1.) Wait it out. Ask yourself, ‘is this urgent and important?’ If not, take a beat…you and I will be better off with this expectation set now,” the email begins. This one stands out because it’s extremely detailed, manages expectations and also offers who to contact in different situations. It models good behavior of taking time off, but also gives the original sender a variety of option. Most importantly, the responder forces the original sender to assess whether this is actually an urgent request.