There are no surname Bennett / Bennet with a given name James or David.
Closest possible match:
Thomas J Smith's Company, Texas Mounted Volunteers - First Service: Composed of personnel recruited primarily from Navarro County. Mustered into federal service 2 August 1846; mustered out of federal service 2 February 1847.
J T Bennett (could be I T Bennett), Private, age 21 years
Another possibility:
2nd Regiment of Texas Mounted Volunteers (George T Wood, Colonel) Organized June 1846
Company K (Robert K Goodloe, Captain) Comprised of personnel recruited primarily from Lamar County. Mustered into federal service 2 July 1846; mustered out of federal service 5 September 1846.
Adam J Bennitt (another source has Adam J Bennett,) Private - promoted 2nd Lieutenant 30 August 1840
Have you seen the source linked below?
M C