I'm probably not going to help much, but here is what I have.

My gg-grandfather, Philip Gathings lived in Hill County. At age 44, he enlisted in Aug 63 and reported to Camp McCulloch in McClendon County. He was in Company B of the 28th Battalion of Cavalry, TST. In Sept, the battalion was sent to Galveston and was under the command of General Tom Green. Their duty included patrolling the west end of the island to warn the city if Federal troops landed. They were also supposed to oppose any landing and failing that, harass and impede the Feds as long as possible. In November, Philip's battalion was merged with other companies he was now in Company A of the 4th Regiment of Calvary, TST. When his 6 month enlistment was up in February, he received a 30 day furlough approved by Brig. Gen. Tom Green, commanding. Up to this time, his service is fairly easy to follow because I have the furlough and several letters written to AND from his wife while at Camp McCulloch, Millican, Harrisburg, and Galveston.

In March 1864, Philip reported back to Camp McCulloch and his company became Company G of the 1st Rgt Calvary, 2nd Brigade, TST. They were sent to Camp Murrah near Tyler in case Gen Steele decided to enter Texas from Arkansas or Gen Banks was successful taking Shreveport. We all know how that ended.
The only record I have of this service is the one Company Muster Roll of April 1864. If I had my guess, after the Red River and Arkansas Campaigns failed, the TST troops may have been furloughed or discharged soon after.