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.
There’s a grim, apologetic vibe to these messages — I’m sorry I’m taking time for myself but I’ll try to check in on occasion! They’re a vivid reflection of a work culture that valorizes constant productivity and the near-total overlap of work and life. But they’re also do a terrible job of what they’re intended to do, e.g., set realistic expectations for both sender and recipient. A vague OOO message traps both parties in an uncomfortable liminal space where both productivity and rest go to die. The original sender is left unsure if they’ll be getting a timely response or a whether the email will go ignored for a time or forever. The original recipient has taken what is a rock solid excuse (time off) and cheapened it, offering a backdoor for email guilt to creep in.

Hijacking this with a question- what do you do when you no longer have an co-workers to serve as an out of office contact? I find myself putting up the OOO less and less, because there’s no one left to respond to anything in my absence (beyond my supervisor who has no knowledge of how to do the tasks of my job).
I work in a culture where even when you say you won’t have access to email, you are expected to be checking. I include this only on the internal auto-response, so that the people in my company know that when I say I won’t have access to email (which is also explained in the email), I mean it. Nothing else seems to work.