There is a Tim K. Seago buried in Board Church Cemetery, Comanche County, identified as belonging to the 3rd Texas Cavalry (South Kansas-Texas Regiment) and with the dates you have provided. Is Tillman his proper first name?

You can order his service files by clicking on the link at the top of the page.

There is a capsule history of the unit provided by Joseph Crute, Units of the Confederate States Army, as follows: The 3rd Texas Cavalry Regiment, organized at Dallas, TX, in June, 1861, contained men recruited at Marshall, Henderson, Ladonia, Greenville, and Dallas. It was also called "South Kansas-Texas Regiment", probably because it was organized to serve in Kansas. It fought at Wilson's Creek and in October, 1861 had 38 officers and 669 men present for duty. Later the unit fought at Chustenahlah and Elkhorn Tavern, then moved east of the Mississippi River. After participating in the Battles of Iuka and Corinth, it was assigned to Ross' Brigade and served with the Army of Tennessee during the Atlanta Campaign. The regiment skirmished in Tennessee and ended the war in Mississippi attached to the Department of Alabama, Mississippi, and East Louisiana. It was included in the surrender on May 4, 1865. The field officers were Colonels Robert H. Cumby, Elkanah Greer, and Hinchie P. Mabry; Lieutenant Colonels Giles S. Boggess and Walter P. Lane; and Majors J.J.A. Barker, George W. Chilton, and Absalom B. Stone.