When making your financial calculations do not count any “final bonus” or withheld amount. The school will try its utmost not to pay that. If you are not in Taiwan by July 1 you will have 20% income tax withheld and you will not get it back. If you arrive before then you will still have it withheld, but you will get 14% of it back. That is roughly the situation. The tax office and immigration deliberately don’t talk to each other. If you pay taxes the tax office doesn’t care about your immigration status. If you have paid your taxes like a good boy, it cuts no ice with immigration.
If you can get by on less than NT$1000 a day excluding rent, you are doing well. I know it is possible. I used to know some very thin and sober people who managed it.