I can help you eliminate-- Joseph E. Johnson age 27 enlisted in the 8th Cavalry, but there are no indications he died. However, it is possible, as they had a rather rough time of it the last 8 months or so of the war, and rosters online do not always indicate death. (Per rosters on-line of the Tennessee Adjutant General). The Joseph H. Johnson who enlisted in the 6th Inf was 23 and too young, and Joseph M. who enlisted in the 10 Cavalry was too old. Most likely he served in the Union. Per information obtained online, men of McMinn County most likely served in the 9th or 10th Cavalry, or the 5th and 7th Mounted Infantry. You do not indicate your location. Civil War muster rcords are on microfilm and located at the Allen County Library, Fort Wayne, Indiana. Also in Knoxville, Nashville, and Memphis, Tennessee, in the genealogy libraries. Best you can do is start by process of elimination.