As I understand it, since FL has no State income tax, a person may execute an affidavit called Declaration of Domicile in a county, which effectively establishes an address in that county as the person's legal home for tax purposes. The person then is required to keep records to support proof that he/she is complying with the Florida rules regarding the Declaration of Domicile. i.e. establish bank accounts, have doctors there, credit card purchases records, and be physically present in the State for 183 days (the greater part of a year.) All of this is required so a person doesn't use Florida as a tax-evasion haven.

What interest would the State of Florida have in a case where it is almost certain the person who executed a Declaration of Domicile has not fulfilled the 183 day residency requirement, and likely has a lack of other supporting records as well, and is likely sheltering a significant amount of income from another State?

I speculate that Florida does not much care unless they are fraudulently claiming a homestead exemption on their property tax.  I think the state in which the party is avoiding state income tax, might be more interested.

Florida will care if you actually do establish residency and do NOT get a FL DL, registration and insurance.

You may be considered a resident of Florida when you:

Have started employment or engaged in a trade, profession, or occupation in this state.
Have enrolled your children in the public schools of this state.
Have registered to vote in this state.
Have filed for homestead tax exemption on property in this state.
Have lived in this state for a period of more than six consecutive months.

As a new Florida resident, you must obtain a valid Florida driver license within 30 days of establishing residency to drive on Florida roads.  In addition, you must obtain insurance from a Florida insurance agent that is licensed to sell insurance in Florida in order to title and register your vehicle(s), vessel(s), and mobile home(s) within 10 days of establishing residency.

In the example I am describing, the person has a Florida DL and has registered a car in Florida, but it is garaged and driven in the other State. The person appears to spend most of his time living in the other State and there is public record of his physical presence in the other State in a pattern that would make fulfilling the 183-day Florida provision quite impractical. Of course everything might be legally solid, but the circumstances cast doubt.

Well, I think we are back to Florida not caring but the "other" state getting butt hurt, that they are not getting their state income tax.

It sounds like you have a reason that you want to make this person's life difficult.  If you have a good reason and are not just looking for petty revenge then you may want to see if the other state offers a reward for tips on tax cheats. BUT, think long and hard about what you may be getting yourself into.  Revenge is a dish best served cold.

A 50 cal BMG round can bounce off of a rock 200 yards away and come back and hit you in the head.  Be careful what you are shooting at, and what is beyond.

No one is going to waste the time to go after the guy in FL.  There are thousands of people that do this in Florida.