Available evidence tends to support two different men by that name. James Aaron, Co. A, 34th AR INF, enlisted on 16 Jun 1862 in Washington County, and James Wilson Aaron/ Aron/Arnn, CO F, 36th AR INF, enlisted with his brother, George Samuel, two days later, 18 Jun 1862, in Conway County. The 1860 census supports this as well. James of the 34th appears in the 1860 Washington County census with his wife and children, while James of the 36th appears in the 1860 Conway County census in the household of his father, Abihu Aaron/Aron/Arnn.

Both men survived the war. James of the 34th died 18 Jan 1874, buried in the Elm Springs Cemetery, Washington County, Arkansas. James of the 36th allegedly died 22 Nov 1886, burial place unknown.

Sources:

Edward G. Gerdes Civil War Homepage, research by Bryan Howerton

Find-A-Grave

Contributed family tree of James Wilson Aaron – Ancestry.com

James Aaron household, 1860 U.S. Census, Elm Springs TWP, Washington County, Arkansas population schedule, page 230, stamped page 707, lines 24-27, dwelling 1579, family 5, National Archives micropublication M653, roll 52, Ancestry.com image 1

Abihu Aron household, 1860 U.S. Census, Griffin TWP, Conway County, Arkansas population schedule, page 129, stamped page 571, lines 23-28, dwelling 878, family 878, National Archives micropublication M653, roll 39, Ancestry.com image 2