Moving abroad for new job this summer – Where to establish 183 days residency for the year?

Dear internet,

My wife and I accepted jobs abroad and we will be moving from Utah (US) to Taiwan. We we will be selling our house in Utah. Since we're both teachers, we have the freedom to move anytime in July, giving us the choice between establishing 183 day residency in either Taiwan or in Utah (or neither).

I know that for Taiwan, foreign worker's income tax will go from 18% to about 5% if you make the 183 days. That would apply for paychecks starting from September onward (so only 4 months of this tax year). But the bigger questions I have are about would happen to my Utah tax return:

1. My Utah paychecks will keep going until August. Will I be better off if I file my Utah taxes with or without 183 day residency?

2. We will be selling our house without buying a new one for now. We aim to start off renting while abroad. Will I get taxed differently on this sale (I think this may be called Capital Gains?) based on establishing 183 days residence? Which one would be favorable? (This house has been our main – and only – home for the past 7 years.)

Apologies for my financial illiteracy – I was never taught about this and am only now trying to figure this out.

Thank You!