William Day was born 11 February 1801 and was the son of Ammery and Nancy (Brown) Day. This couple also had sons named Larkin and John.Larkin later used the surname Henderson, adopted from his step-father; he married and raised a family in Hampshire Co. John may have married and had a son, but if so, John died by 1850.
William Day sold land in in Hampshire Co., VA to Ransom Day in 1811.This land was adjacent to Thomas Henderson's land.Ransom Day also purchased personal property from Ammery Day in 1815.Given these transactions, and the fact they were next-door to Thomas Henderson, there must be a connection.
The "smoking gun" for the father of William Day (b. 1801) is:
“Amrey Day appointed guardian for his son, Wm. Day, whereupon he gave bond, the said William having made choise of said Amsey [Amery].”(Hampshire Co. Minute Book, Vol. 2, p. 24, 19 Aug. 1817)
William Day (1801-1873) may have been a blacksmith... can't say for sure... but he inherited smith tools from his grandfather, Alexander Brown (d. 1816 Romney, Hampshire Co., VA/WV)
https://www.genealogy.com/forum/surnames/topics/day/7815/