I have a fair amount of information on this line. What follows is from memory, since i don't have my research materials in front of me:
the William Gascoigne you reference did not die in 1672 as you mention, but later. In fact, he is most likely the same William whose estate was administered in 1692 or thereabouts by a grandson Robert (son of his son Robert). William was married to an Elizabeth (surname unknown).
William had two sons, Robert and Henry. Robert, the elder of the two, was born around 1647, married a woman Elizabeth (surname unknown), and had two children Robert and Bridget. Robert, Sr. died around 1675.
William's younger son Henry was born in the early 1650s, and died sometime around 1691-2. Henry married Elizabeth Fisher, daughter of Capt Phillip Fisher of Accomack, and left 4 sons (Henry, William, Thomas and John) and at least one daughter (whose name escapes me at the moment).