I think you'll find it in The Githens Family in America. (I just spent a few hours poring over the book.) Henry Githens only appeared with the Gitthens spelling once I think, and his descendants didn't use it at all.
It's interesting that the John Githens with the two wives and so many children had a son named Henry W., born in Kentucky between 1810 and 1820, and my ancestor, also Henry W., died in Nicholas County Kentucky in 1815.
A third Henry W. shows up, too. Sherwood Githens attributes the children of my Henry W.'s son Valentine (born in 1798) to a George-line fifth generation Edward, who was the son of a Henry W. born in 1823 in Indiana. My g-g-grandfather, Thomas E. Githens, is one of those children,and he was born in 1826!
What a shame that the census didn't start listing all family members until 1850.