There is one Daughters of the American Revolution Magazine, Vol. 53, R.R. Bowker Company, page 575 that indicates a DAR record for a John Parker being the son of Nathaniel Parker and his wife, Ann Clayton, but it does not say he is the Elder John Parker. This DAR magazine article then states: She is SUPPOSED to be a dau of John Clayton and Elizabeth Whiting. (See: https://www.google.com/books/edition/Daughters_of_the_American_Revo... )
There are multiple Sources which state that Anne Clayton, the daughter of John Clayton the Gloucester Co., VA. botanist and his wife Elizabeth Whiting were the parents of an Anne Clayton, but that Anne Clayton was born abt. 1746 and married Henry Landon Davies on 15 Jan 1767 in Gloucester Co., VA.
SOURCE
Genealogy Trails History Group - Early Family Biography - The Clayton Line (See: http://genealogytrails.com/vir/york/bios_early.html )
Genealogies of Virginia Families: From Tyler's Quarterly, Vol 1 - 1981, page 97 Davies-Clayton (See: https://www.google.com/books/edition/Genealogies_of_Virginia_Famili... )
Encyclopedia of Virginia Biography Vol. 4 page 158, by Lyon Gardiner Tyler published 1915 Anne Clayton, daughter of Dr. John & Elizabeth (Whiting) Clayton ( See: https://archive.org/details/encyclopediaofvi04tyle/page/118/mode/2up )