This could be a possible lead to your John Pittman (bc 1726).There was a John Pittman (son of Joseph (bc 1700), grandson of Obed (male), and g-grandson of Joseph Pitman of Accomac Co. VA. (spouse: Elizabeth Johnston)).
The only researcher for this line - that I know of is - Bob Pittman Greenville, NC firstname.lastname@example.org
The Joseph (Accomac) line and the Capt. Thomas (Surry) line are - DNA wise - very closely related.
Descendants of this Joseph line from Accomac Co.eventually moved to Craven and Lenoir Counties, NC but I have no clue about John.