Sorry - don't know about TN MV laws.
In Florida, because of the weight of my M931, I am required to declare the GVW of it, any trailer it will haul, and any cargo thereon (in my case, as it weighs 22K, I declared 43,999 which required 100K liability insurance. If I have gone to 44K, it would have triggered a 300K limit).
Florida has conflicting statutes regarding definition: One says a "commercial vehicle" is anything with three axles "regardless of use". But another statute defines a CMV as engaged "in commerce".
I obtained a very reasonable Commercial Insurance policy for the 931 from Gulfway in Florida (they advertise in AHTA magazine).
If TN is interested in USE, then that initiates one response. If they are interested in WEIGHT or AXLES, or "VINTAGE" (as in antique, etc) those may be additional responses.
Some states have a problem with military vehicles because of their former use - but in Florida they meet all the requirements for being "street legal" - I even put a set of removable flaps on the 931 to be compliant, and of course I have a Class A CDL so driving the tractor connected or otherwise is not an issue.
Tagging and titling for me was a breeze. Good luck.