Jesse Russell, Private, Company C, 32nd Mississippi Infantry, deserted, captured and subscribed to the Oath of Allegiance to the United States, December 5, 1864 at Nashville, Tenn., resident of "Pike County, Miss.", dark complexion, dark hair, grey eyes, 5' 8".

I'm finding two more residents of "Pike County, Miss" in this same company and regiment who also deserted at the same time as Jesse Russell.
John W. Simmons and Henry Simmons, I believe this Henry Simmons was a brother-in-law of Jesse Russell.

I know it has been a year since you first posted, have you found any additional data?