I do no work in either state and I own homes in both. Michigan is my state of residence. I sold my Michigan house where I had lived for 28 years and bought a manufactured home in a 55+ community. My Florida home is a Park Model trailer in a 55+ community.
I have questions as to what I can claim for property taxes for all three homes
I'm presuming all of these properties are personally owned and not rental and/or income producing. You can claim state property taxes both real estate and personal (cars, mobile homes etc) and state income taxes up to the new tax law limitation of $10,000 total. If your total of Schedule A deductions (state income taxes, mortgage interest, property taxes, charitable contributions etc) don't exceed $12,000 if single or $24,000 if married filing jointly, you'll be better off just taking the standard deduction and not filing Schedule A. TurboTax will determine that automatically after you enter your deductions. The limitation does not apply to rental properties. Taxes are considered a business expense for those.
What impact does splitting my time equally in two states have on state taxes?
Do I claim only the earnings (pension benefits) received while in the respective states?
@wasoki - The original post named MI & FL. I'll use those as example.
If you lived and worked in MI, prior to retiring, and now split your time between FL & MI, for tax purposes, you are still a full year resident of MI and will MI tax on all your income.
Let's say the 2nd state (unlike FL) also has an income tax (I'll use SC as an example). You are still a full year MI resident and only pay MI tax, unless you do something specific to change your residence (car & driver licenses and voter registration).
It also depends on the specific states. NY in particular has strict residency rules. If you maintain a residence in NY, you will continue to pay NY tax, even if you change your voter registration, etc. Check your state(s) tax agency web site for specific residency rules.