Here's some info that perhaps someone better versed in genealogy might use to track him down. I hope this is of some help.
From the Confederate Graves Registry - Jackson was born 10/19/1823 and died 12/12/1871. His wife was Margarette (Graves). Jackson served in Co I of the 7th MS Cav.
The 1860 Census has him living in Saulsbury, Tippah County, MS with his wife Mary (20) and children, Maggie (5), William H (3), and George (1).
The 1870 Census has the following in the household:
G B Jackson 46
M G Jackson 30
M L Jackson 14
W H Jackson 13
Geo R Jackson 11
Lucius E Jackson 9
Ida Jackson 5
Walter W Jackson 3