I see that T.H.Clay is listed in Colonel Parson's Order book as one of 19 soldiers of various companies the 12th Texas Dragoons detailed to remain in camp and act as witnesses before a Genl Court Martial.

Special Order No.58
Head Qrs White River Dist.
Lake Bluff Ark Decr 4th. 1862

He is listed as JH Clay but this is probably him and only an error in transcription as much of the original order book preserved in the Waxahachie Library is difficult to read. Not much to add to his only two surviving muster roll cards but at least this tells you where he was at a certain time and adds a little to your info.

Ann Bailey transcribed the Order Book in 2004 and had it published as,"In The Saddle With The Texans,Day-By-Day With Parson's Cavalry Brigade,1862-1865."

Do you know where he lived before the war?