Gideon Pulliam - Gragg-Pulliam family

On many charts, including here, William Obadiah "Revolutionary Bill" Gragg, Jr. is listed as married to an Elizabeth Pulliam, daughter of Gideon Pulliam. He is often placed as a son of John Pulliam. I have found no documentation of this link, or of the existence of this Gideon and Elizabeth. It is clear that William Obediah Gragg had most of his kids from an unknown first wife before marrying Nancy Coffey late in life, but I can't find any evidence her name was Elizabeth Pulliam.

Further, John Pulliam left a will that named all his children including an unborn child that later probate records show is Joseph Pulliam. So unless Gideon is actually the middle name of the William, Joseph, John or Drury mentioned in John's will, it is doubtful he is a child of this John Pulliam.

There was a Gideon who was the son of John's son John Jr. But that Gideon was too young to be the father of William Gragg's first wife. My suspicion is this older Gideon never existed. Can anyone find evidence to the contrary? Otherwise I think he should be severed from John Pulliam.