Offhand, there were two brigades, Reynolds' and Vaughn's, that participated in the Vicksburg Campain, that were made up of East Tennessee Regiments. I am more familiar with Vaughn's, which had the 60th, 61st, and 62nd Tennessee (one of my ggg granfathers was in the 62nd). While the 62nd fought well at Chickasaw Bluff in December 1863, many of the men in the brigade were volunteers only in name, were Unionists, and joined up in the last half of 1863 to avoid constription (which was about to be reinstituted in East Tennessee). Vaughn's Brigade broke quickly while acting as the rear guard at the Big Black River, following the battle of Champion's Hill. After the surrender at Vicksburg, it appears many of the men of these three regiments did not return to their units once the regiments' parole periods ended. Some, including my ggg grandfather, ended the war in Union regiments (in the case of my ggg grandfather, the 3rd Mounted Infantry, then the 8th Infantry).

Vaughn's Brigade was mounted after the parole. The brigade was one of five cavalry/mounted infantry brigades that acted as escort for Jefferson Davis when he attempted to escape west (another was Ferguson's Mississippi/Alabama brigade, which had included my Weatherford ancestors)

A good book on the topic is Mountain Rebels.