It's a long shot, his widow's pension application papers might provide the information you seek.

Benjamin J. Long

Residence was not listed; 33 years old.
Enlisted on 12/10/1863 at Fort Smith, AR as a 1st Lieutenant.
On 12/10/1863 he was commissioned into "D" Co. AR 2nd Infantry
He Resigned on 6/3/1865
(His widow applied for a pension in 1882)
Sources used by Historical Data Systems, Inc.:
- Index to Compiled Military Service Records
- Official Army Register of the Volunteer Force 1861-1865
- 2nd Arkansas Union Infantry - Arkansas Research