This man was actually a member of the 5th Texas Infantry, Co D. Here is a short service record compilation from the Texas Brigade reenacting site at:
HILL, WM. T. Captain Orig. 1Lt., Co. D: Detailed to recruiting duty in Tex., Feb. Apr., 1862: Prom., Capt., Aug.23, 1862: W. (foot), Gettysburg (July 2, 1863): W. (arm), Wilderness (May 6, 1864): Paroled, Appomattox (Apr.12, 1865) as Cmdr., 5th Tex. Inf. Regt.
You may also obtain his Compiled Military Service Record through this website by clicking on the link below. I've looked at it and it is 101 pages of information.
With best regards,