It’s also a logistical problem.
The OP wants to land a short-term job (though of course I suppose it would be possible to take a long-term job and simply break the contract at the end of the summer, if it were possible to find one quickly in the first place). OP also wants to be studying at a language center, which means taking whichever hours are offered, usually (it’s rare to have a choice of hours at your level and also to have the center respect the choice).
OP could potentially just find a tutor, which solves the set hours problem, but then the question is a visa, unless OP has visa-free entry or can get a visitor visa from the home country and is potentially willing to make visa runs (which means more money).
OP does not mention any previous Mandarin experience, but even if there is some, I would really question the value of a summer in Taiwan if most of OP’s free time was going to be spent wrangling children in English. It just doesn’t make sense economically or educationally IMO. If the OP has just graduated and has no obligations in the home country, my suggestion would be to work for the summer or beyond in the home country first, save up a bit of money, and come to Taiwan to study Mandarin for a couple of months without working, when it’s possible to just study and not teach at the same time. It’s unlikely that OP is going to get much in the line of Mandarin practice through a teaching job.
I guess it depends on the OP’s goals for Mandarin, though. If the idea is to become proficient, summer isn’t going to do much for that anyway.
One important point is to choose the least expensive language program that can still provide a visa if that’s needed. Structurally and results-wise they are all pretty much the same, use largely the same materials, and do things the same way.