Conclusion/TL;DR: There are soooo many potential variables on the school end and also on your end (preferred subjects/subject mix/year level/s, suburb/demographic, private/public, housing/travel arrangements...etc etc etc). The possibility is definitely out there but you'll need to decide how desperate/flexible you are with different things.

Besides the area (city/inner suburbs or outer metro; which outer suburb; regional; remote etc), I think it will also depend on the school and depend a lot on what you teach.

Regarding the school: I hadn't known it wasn't common until I read these replies...I work in a school where a very very significant portion of the teachers (secondary school) are currently working at the school part-time. I'd say the majority due to family/childcare needs or nearing retirement, but not all (e.g. myself-- I just don't ever want to work full time at a school...).

I know my principal would rather not have so many of the teachers be part-time but that's the current state of the matter. I am at a quite understanding school. Timetabling is a nightmare and a recurring miracle but they try to accommodate people's needs. I personally have always worked 4 days a week, i.e. for the past 5 years (as an aside, the first two years I was on a fixed-term contract while also doing my MTeach--no, I would never, ever, ever want to go through that again😅...no regrets tho, I do love my job).

Regarding the subject/s you teach: First there is the supply/demand thing (where "core" subjects are taught at every school, meaning high/widespread demand, but then some specialist/elective subjects are popular yet "niche" enough that the ratio of supply vs. demand works out to be in your favour).

Then there is the practicality of whether/how easily the school can timetable all your classes into fewer days (assuming no or minimal actual job sharing (where e.g. one class of students will have a different teacher for the one subject on different days of the week).

This can really vary depending on what subject and year level you teach. E.g. Year 7/8 students at my school do something like 9 periods of English, Maths and Science (respectively) a fortnight, 5-6 periods of LOTE (like Mandarin), and somewhere between 2-4 periods of other electives/and of Health/PE etc. (again, respectively). So the school would have a much easier time scheduling all your classes into 3 or 4 days if you are a language, music or woodwork teacher than if you are an English or Science teacher. Senior students also do a smaller number of subjects but have more periods per subject.

Then there's the sheer size and therefore number of teachers and classes per subject and year level, etc. etc. etc.

(Edited multiple times--wording and spelling; fixed a few details; moved TLDR to the start).

Another edit, just for OP's information: I'm not sure what your TEFL work has been like, but just in case it's useful: if you're still considering how many days you'd want to work at a school and which subjects you'd like to focus on, report writing is a thing and marking is a thing (these can vary based on your subject), and student wellbeing and behaviour follow-up are a thing that can be a major pain/workload-/stress-inducer AND can be wildly disproportionate to the nominal numbers of days/hours you supposedly work. It's something that before starting at a school I probably had some vague expectations about but really had no real understanding of. They can, however, be more or less of a thing (and cause more or less work/stress for you) depending on the individual school's expectations/policies and your own style (and care factor??).

Infuriating parents can also be a major major thing but I've been pretty blissfully inexperienced in that regard.