Just a guess based on Thomas Brannon being one of only 2 Brannon's in Jackson Co,TN in 1803 Tax List, pg 114 of "Ansearchin News". He is in Capt Shell & Shaw's district (southwest part I believe). John Brannon is in Hay's district which was probably the central northern part of Jackson County.
http://www.tngs.org/ansearchin/pdf/1995-3.pdf
Brannon is an Scot-Irish name, and I see other Irish Brannon's with Thomas and Nancy names. Brennan is the most common surname in Kilkenny, Ireland.
Curious coincidences:
Nancy Brannon Green's son John named a son "Sampson McClaron Green". A Brannon family in VA that had Thomas and Nancy names in it descends from an original immigrant ancestor named Caron Branhan, 12 yr old endentured servant to George Davenport of Richmond, VA! Some descendants went to Johnston Co, NC where in the marriage records are found:
James Brannan & Rose Martin, 27 Jan 1783, William Green, bm.
Leroy Brannon & Rebeckah Cole, 4 Oct 1791, William Brannon, bm.
William Brannan & Mary Green, 27 Nov 1793, John Watson, bm.
Caron Brannon & Milly Green, 1826
kdd: Perhaps the Green's & Brannon's of Jackson Co, TN came together from NC.
If you found a relative, please sign my