Best suggestion is to use a friend or relative's address for proof of residency or a paid address that uses a real street address rather than a PO box in Tennessee. If the UPS location you mentioned uses a street address rather than a PO Box address you are ahead of the game as a PO box is not acceptable for a driver's license and some other things in Tennessee. Tennessee wants your sales tax so spend handsomely when you are back home in the "Smokies"! We don't care about your EARNED INCOME cause we know your going to spend it all so SPEND IT ALL HERE IN TENNESSEE!
State Income Tax "Can" become a sticky issue if your legal residence is Tennessee and you choose to earn an income (WORK & GET PAID) in another state besides TN and that state has a state income tax. They are gonna "Want Their Money" for your labor. New York as an example is tough on folks making a living in New York and claiming a residence elsewhere.
As an example many states with a State Income Tax will make a professional sports athlete pay state income tax on any income derived from playing a professional sport in that state in which they earned income if that state has state income tax. Something to consider!
One of many items to declare a state of residency is the 183 day rule for residency however since you will be traveling that won't work.
I suggest you look at the sites below as there are many more things you can do to make certain to prove to others your true State of Residence. Do a Google search as there is LOT'S of information out there to answer your questions.
https://axleaddict.com/rvs/Full-Time...tate-Residency
https://rvshare.com/blog/state-residency/
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