Roster of Confederate Soldiers, 1861-1865 does not show a William F. Gibson, or any William Gibson.

Roster of Union Soldiers, 1861-1865 does not show a William F. Gibson but does show:

Gibson, William KY 1st Cav. Co.D
Gibson, William KY 8th Cav. Co.G
Gibson, William KY 9th Cav. Co.I
Gibson, William KY 5th Inf. Co.B Cpl.
Gibson, William KY 21st Inf. Co.E
Gibson, William KY 23rd Inf. Co.F
Gibson, William KY 26th Inf. Co.B
Gibson, William KY 28th Inf. Co.F
Gibson, William KY 30th Inf. Co.C
Gibson, William KY 39th Inf. Co.F
Gibson, William KY Vol. 1st Bn. Louisville Prov.Guard Co.I