All brothers and sister of John Cunningham had a middle name. John is the only one that didn't have his middle name listed. In the 1860 census it is only listed as John Cunningham. My aunt did extensive research on the Cunninghams in the 1940's. She lists him as John S. Cunningham (1830-1912). Yes, it could be wrong, but we find it odd that he had no middle name. It would have narrowed the chase to have a middle initial, because there were close to 500 John Cunninghams in both armies. Of course, your research will prove this wrong also.
We are also related to the Sevier's. It is a good guess that this middle name might also be Sevier. Yes, I could be wrong. I am not the consumate profesional you are. Franklin L. is probable a relative, but not a brother. His brother was Francis Franklin Cunningham. From my grandfather's testimony, half of the brothers fought for the Union and half for the South.
Documented Mordicia - father Union
William H - son Union
Prior Essex - son Union
Calvin Jones - son Union
Undocumented
Francis Franklin - son unknown
John - son unknown
Joseph O. son unknown
James P. son unknown

Yes, I'm sure there are errors. The Cooks, Davis's, and Burchett's are closely related and they all fought for the South.
Oral history says that one of the brothers rode with Ashby, but I have found no evidence.
There were 2 companies that were formed in Carter's Cavalry that were Claiborne Co and, to the best of my knowledge, there rosters have not been found. Of course, you would know better that me.

From what I have observed, I still don't know John's military history.

Sorry I'm so ignorant!