The service file includes Bright's statement that he deserted Apr 18, 1864, and took the oath of allegiance at Nashville TN, Jan 24, 1865. The only roll on file reports him absent on detached duty, May 20, 1864. If his statement of Jan 1865 regarding date of desrtion is even close to being accurate, participation in the Battle of Franklin (Nov 30, 1864) would not seem possible.
Have you seen this man's military service file?