In Japan "一身上の都合により" is the standard phrase used on resignation letters when an employee quits. It means leaving for personal reasons, & you can just use that.
Yes, this.
BUT I have to remark--if you've been signing contracts for 20 yrs then I think, given all that's been written about it, you are a de facto permanent employee (seishain/正社員)--and if that's the case, there may be other options open to you besides just resigning.
I don't want to be nosy, but if your reason for thinking you need to resign is something that can be taken care of over a few months or so (eg, illness of someone back in your home country), you may be able to take some kind of leave.
If it is you that is sick, and you're anticipating an extended hospital stay (thinking you will be unable to work), you may simply be able to present your medical diagnosis (shindansho/診断書) to the school, and you should be able to be absent from work for the duration of treatment (and your doctor's authority would likely not be questioned).
Further, if you happen to be a member of the uni mutual aid association, after something like two months(?) off your school will stop paying you and the mutual aid assn will take over, probably with approx 2/3 of your salary.
Edit: If you are indeed full time/seishain, your reason for leaving the job can have an impact on the severance that you might receive (退職金). This is often calculated as a multiple of the years of employment, and the lowest multiple is used when the employee quits--resigns on their own. Tho I don't know what's in your school rulebook (規則書), there could easily be a chart in there that specifies the amount of severance (given a certain number of years worked),
based on the reason for separation.
Reaching retirement age is often the highest multiple, and simply resigning is the lowest. If you are leaving for medical reasons, there may be a category for that which is between those two.
Even if you do end up simply resigning, if your actual employment status has been seishain, you may be entitled to even the lower level of severance payment associated with that (vs. thinking you're on contract, and there will be no severance).