I rarely quote Fold3 as a source, using however, their source, the NA Compiled Service Records, i.e.,
M268: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Tennessee
Nonetheless, you're looking at the wrong 3rd Tennessee Infantry. You want Lillard's, formerly Vaughn's, East Tennessee foot soldiers who served in Col. A. W. Reynold's East Tennessee Brigade at Vicksburg.
Post Vicksburg, they were transfereed to John Crawford Vaughn's East Tennessee brigade who had them mounted ca Nov.,1863. They served thereafter as a Cavalry regiment. Although, they might have served essentially as a mounted infantry unit, they were entitled Cavalry.
In general, we usually find out their Galvanized Yankee service through Federal paper work from POW records at Northern prisons, such as Camp Douglas, Chase, etc.
If he enrolled in a Yankee unit in East Tennessee, intelligence as to his past Confederate status would usually not be identified.