Hey Dennis,
Was his wife's name Francis? If so I found him as Samuel Harper age 23, born in Mississippi on the 1860 census, living in Covington County. The only S. J. Harper listed on the 1860 Mississippi Census was living in Rankin County and was 18 years old and female. Another Samuel was living in Rankin County at 32, and Monroe County age 18. No other combination of S. J., or Samuel J., or Samuel Jackson, or Jackson with a Harper surname is listed. So the process of elimination says it must be him. Many men just south of Simpson County came to Westville (now nothing but a cemetery) to enlist and join in companies. From there they marched over to Hazelhurst to catch the train to Jackson. Many from Lawrence and Covington Counties joined up in Westville. I have a S. J. Harper listed under the Simpson County records as a corp. in the Simpson Greys but in the same regiment I have also a Samuel Harper, private in Company F, Pearl River Guards of Simpson County. no other information. Could be the same fellow, they did transfer between companies.
You can go here if you want to see the military records I have.
http://home.bak.rr.com/simpsoncounty/
David