Harold,
I did a real quick look at some sources and didn't find any military info on a Thomas L. McNatt. However, a couple suggestions I do have is to come up with any spelling of the surname that you can think of. Also, is it possible that he went by his middle name at some point? Then I would start with the NPS Soldier and Sailor listing and search for all the possibilities that you come up with. This is an excellant starting point. I did see his headstone on findagrave and I see that he is listed as being with "Confederate States Army" and not a particular state regiment. This might point you to looking into CSA regiments instead of regiments from a particular state. If you come up with some possibilities from the NPS listing, footnote.com has many CSA records. Hope this helps a little - good luck!