George,

I certainly wouldn't discount your source, the format is identical to that of the NPS Soldiers & Sailors System, however, I cannot find his name in any Texas Unit therein, nor could I find a separate Parson's Brigade except for the CSRs for the 12th Texas Cavalry.

Try a Goggle Search, "Parson's Brigade" Here are two snippets I came across.

Dean is not listed on the F & S for the 12th.

I'll be heading to the library a little later this morning where I will be able to check the Texas CSRs via the regiments noted. (You can order these service records from the link below or through the ad at the top of this page.)

George Martin

Parsons' Brigade

12th Regiment Texas Cavalry

Field and Staff Officers

Colonel
William Henry Parsons

Lt. Colonel
John W. Mullen
Andrew Bell Burleson

Majors
Emory W. Rogers
Locklin J. Farrar

R. A. Terrell, Captain
Commissary
Adjutants
William G. Varnell
Andrew Bell Burleson
William M. Davies

PARSONS'S BRIGADE. Parsons's Brigade, a Confederate brigade during the Civil War,qv was organized in the autumn of 1862 to serve as cavalry for the Army of the Trans-Mississippi then forming in Arkansas. For much of the war the brigade was commanded by Col. William Henry Parsons,qv who had raised the Twelfth Texas Cavalry Regiment in the summer of 1861. In late 1862, however, Brig. Gen. James M. Hayes briefly commanded the brigade, in 1863 Col. George W. Carterqv led part of the regiments, in 1864 Brig. Gen. William Steeleqv assumed command, and in 1865 Parsons regained total control. Because the force had been organized under Colonel Parsons, served under him in 1863, and was again under him at the end of the war, it was generally known as Parsons's Brigade. The permanent components of the brigade were Parsons's Twelfth Texas Cavalry Regiment, Nathaniel Macon Burford'sqv Nineteenth Texas Cavalry Regiment, George Washington Carter's Twenty-first Texas Cavalry Regiment, Charles Leroy Morgan's Texas Battalion, and Joseph H. Pratt's Tenth Texas Field Battery.