This is just my two cents based on personal experience.
Home of Record will always be just that - the place from which you joined the military. State resident, for tax purposes, something else.
Each state will have info on requirements for residency and how they handle out-of-state active duty military for tax purposes. These days, it's on the state.gov websites.
JAG or Legal Services Office should have some references on state resident and tax issues, as well as official advice.
Most of us current and former military PCSers know the states that have no state income tax. Off top of mind, FL, TX, NH, NV, WA and others I can't remember. Great, if you happen to be stationed in that state and do the necessary actions to meet the requirements to establish residency in that state and tell your old home state buh-bye when they come calling for annual state income tax. You can't just say, yep, I think I'll select FL, with no physical presence or activity to kick-start the notion of residency.
There are some states which do not tax their residents when serving out of state on active duty. Husband was a PA resident, and that was their deal. As a naval aviator, he never returned to the state for active duty, hence, he kept PA as his declared state for tax purposes. Might not be so good for other services which might have duty stations there.
Some states do not tax the FULL amount if their residents are serving out of state on active duty. Again, check the state.gov website.
I, on the other hand, hailed from GA, and they wanted their full state income tax the years I was in Spain and Italy. I wasn't using their roads, schools or other state services, and did not intend to reside there, so as soon as I PCSed to FL, I registered to vote, registered the car with FL DMV, got a FL driver's license and gave GA notice I was now a FL resident. I continued to vote absentee in FL elections for the remainder of my career. I did not retain FL plates or driver's license, but changed that as needed in various states as current plates/license needed renewing.
That all said, first step is to explore WI's deal for active duty serving out of state. Next step, determine what states along your son's projected path might offer a better opportunity for residency and what their requirements are.
Hope that helps.