F. M. Gibson
Regiment Name 30th Battalion Virginia Sharpshooters
Side Confederate
Company F
Soldier's Rank_In Private
Soldier's Rank_Out Color Corpl
Film Number M382 roll 21

30th Battalion, Virginia Sharpshooters (Clarke's)
30th Battalion Sharpshooters was organized in August, 1862, with six companies. The unit was assigned to G.C. Wharton's and A. Forsberg's Brigade and fought in various engagements in East Tennessee and the Shenandoah Valley of Virginia. After the Battle of Waynesborough, it disbanded. Lieutenant Colonel J. Lyle Clarke and Major Peter Otey were in command.

F. M. Gibson
Regiment Name Capt. Carrington's Company Virginia Light Artillery. (Charlottesville Artillery.)
Side Confederate
Company
Soldier's Rank_In Private
Soldier's Rank_Out Private
Alternate Name Tandy M./Gibson
Film Number M382 roll 21

With either one, you need access to the records - which I don't have. Of course, if he is the one listed as this in the 1860 Federal Census:

1860 United States Federal Census
about F M Gibson
Name: F M Gibson
Age in 1860: 9
Birth Year: abt 1851
Birthplace: Virginia
Home in 1860: District 3, Putnam, Virginia
Gender: Male
Post Office: Hurricane Bridge
Value of real estate: View Image
Household Members: Name Age
C Gibson 42 Farmer
L Gibson 46 wife
W J Gibson 19 laborer
J J Gibson 17 laborer
M J Gibson 16
J H Gibson 14
M E Gibson 12
F M Gibson 9
W Henderson 62
J W Forth 20

He would be too young!

Think we need more information.