Allan,

Other sources show the spelling as Gipson as follows:

List of Field Officers, Regiments & Battalions in the Confederate States Army 1861-1865
J. M. Carroll

"Gipson, William-Major 2 Arkansas Mtd Rifles; Major-Gipson's battalion Arkansas Cavalry"

Compendium of the Confederate Armies
Sifakis

"Arkansas [Johnson's-Hawthorne's-Cocke's] Infantry Regiment"........"Reorganized by the consolidation of the original companies and the addition of three companies of Gipson's Mounted Rifles Battalion on Dec. 16, 1862........."

If Bryan says Gipson's battalion had nine companies, then I'm confident he has strong evidence of that fact.

Here are some more references to Gipson's battalion [shown as Gibson]:

Alexander Papers
[excerpted]

July 27
Fort Smith-Col Carroll to Hindman
Major Gibson's command is mustered into the service.... at last report five companies total strength 375 men... with only 170 guns

July 31
HQ Fort Smith-Col Carroll says
so soon as Gibson's command is arrived I will move at once and......... with the mounted force

August 10, 1862
Special Orders Army of the South West #62-
.............
VII. the resignation of 1st Lt J R Fitsworth Co E 1st Battalion Mounted riflemen [Wm Gibson cmdg.] is accepted
......................

August 12, 1862
Fort Smith Col Carroll to Hindman
.........the mounted force is north of the mountain except Gibsons battalion which is on the march to Madison county in obedience to your order to throw a cavalry force in that direction to protect salt peter works in Newton county.......... the battalion is 400 strong with 80 guns............

August 28, 1862
Madison County Arkansas
Major cmdg. 1st bn of 5 cos
some absent with permission of Col Carroll-Major William Gibson

September 5, 1862
Headquarters 2nd brigade Camp Mount Comfort to Gen Rains comdg 3rd brigade
.........................
The Col cmdg. says that Maj Gibson cmdg. Cavy battalion has only 150 guns and reports enemy at Huntsville

Seotember 9 [??], 1862
Colonel Carroll to Hindman
Colonel Brooks with the cavalry battalion has not yet reported. Your instructions in regard to Colonell Brooks and Major Gibson will be obeyed.... I have also directed a portion of my cavy regt to picket the roads leading to Genl Rains camp..... I will have the cav regiment organized as ordered.......................