I suggest you query the Arkansas History Commission regarding his service and possible pension application by his widow.
When requesting information, give veteran's full name, wife/widow's name, county of residence, and military service unit, if
Arkansas History Commission, One Capitol Mall, Little Rock, AR 72201
A E. Bright
Residence was not listed;
Enlisted as a Private (date unknown).
"H" Co. AR 4th Cavalry
A.E. Bright (First_Last)
Regiment Name Gordon's Reg't. Arkansas Cavalry
Soldier's Rank_In Private
Soldier's Rank_Out Private
BRIGHT, A. E. Pvt - Enl 23 Jul 1863 at Bentonville, AR. AWOL 20 Oct 1863. [http://www.couchgenweb.com/civilwar/4thcoh.html]
Gordon's Regiment, Arkansas Cavalry
Gordon's Cavalry Regiment [also called 4th Regiment] successor to C. A. Carroll's Cavalry Regiment, was organized in September, 1863. It served in General Cabell's Brigade, Trans-Mississippi Department, and took an active part in the conflicts at Poison Spring and Marks' Mills where twenty-one percent of the 117 engaged were disabled. Later it participated in Price's Missouri Expedition and reported 106 casualties. During the spring of 1865 it disbanded. The field officers were Colonel Anderson Gordon, and Majors J. A. Arrington and William H. Fayth.