Ken,
From American Civil War Reseach Database;
Elias Brannick age 20 (1863)
Enlisted on 3/31/63 at McDonald Co. Mo,for 3 years
Mustered 3/31/1863
Co. A 1st Ark Cav (US),
Rank in sergeant
Date and method of discharge not listed.
Born Surry Co. NC
Died Desoto,Ks 11/28/1917
Applied for penision 1866

Hope this helps.
Mike