Roster of Confederate Soldiers, 1861-1865, shows:

Brown, William TX 29th Cav. Co.A
Brown, William A. TX 11th Cav. Co.G 1st Lt.
Brown, William A. TX 29th Cav. Co.H Capt.

Sifakis, Compendium of the Confederate Armies - Texas, page 86

29th TX Cav Reg organized July 1862 - dismounted Feb 1865 - surrendered by Gen E.K.Smith 5/26/65 - disbanded at Camp Grace, near Hempstead in May 1865 - had been part of the Trans MS Dept
BATTLES: Fort Gibson 5/20/63
near Honey Springs 7/17/63
Camden Expedition March-May 1864
Poison Spring 4/18/64
Camden 4/23/64
Massard's Prairie, near Fort Smith [detachment] 7/27/64
Cabin Creek 9/19/64

see: Felmy, Bradford K. & Grady, John C., Suffering to Silence: 29th Texas Cavalry, CSA Regimental History