My great-grandfather identified his great-grandparents as John Thompson and Nancy Cawthorne, but thanks to G.L. Thompson, I now know that they appear in the 1850 and 1860 census records as John and Catherine (which accounts for why I couldn't find them previously!) Specifically, the 1850 Union Co. NC census shows John L. Thompson age 61, born Virginia, and wife Catherine N. Cawthorne age 60, born Union Co. NC. This discovery is causing me to revisit earlier data in hopes of finding the link between Catherine aka Nancy and the early Cawthorne family of Essex Co. VA, who I think are her likely ancestors.
My initial source for this family was The Cauthen Family History, by Maryline Cauthen Westenhaver of Auburn Al. This is available on microfilm from the LDS as their #1033898/12. Louise Pyles Castens has written a genealogy of the Cauthorn and Piles families, which includes many transcriptions of wills and other documents.
The immigrant ancestors were Richard Cawthorne and Anne Cox, who married 13 May 1668 in England, and were in Virginia by 1674. Anne was deceased by the time Richard wrote his will, which was probated 2 March 1686/1687.
James Cawthorne, a grandson of Richard and Ann, came from Essex Co. VA to Warren Co. NC about 1767. About 30 families from the Nutbush and Smith's Creek section of Warren Co. NC settled in the Cedar Creek area of southern Lancaster and northern Kershaw Co. SC before 1800, near the present town of Stoneboro. James' sons Thomas, William and James were among them. These are the only Cawthornes that I have found near Mecklenburg and Union Co. NC, where Nancy and John Thompson eventually lived.
According to the Cauthen manuscript, Thomas Cawthorne had a daughter Nancy Agnes born about 1777 who married Robert Campion. William Cawthorne had a daughter Nancy who married William Duke. James Cawthorne had two daughters who were in the range of 16-26 years old in the 1800 census. This would be approximately the right range for my Catherine / Nancy Cawthorne, who was having children in the period between 1809 and 1829. However, there's no proof! Can anyone add any information that would help solve this mystery?