Dear Ms. Keeton,
Thank you for posting your request on History Hub!
The Federal Government does not ordinarily create or maintain birth, death, marriage or divorce records. Such records are made and kept by State and local governments rather than the National Archives.
We suggest that you contact the Texas Health & Human Services for a death verification letter. The letter will state whether a record of death (since 1903) is on file with the State of Texas and will include the person's name, the date of the death, and the county where the death occurred. According to their website, if his death was recorded before 1903, it was recorded in the county clerk's office, so you will want to check there for any records. A list of County Clerk addresses is on the County and District Clerks’ Association of Texas website.
We hope this is helpful. Best of luck with your family research!
I tried to find your Austin but no luck.
If he was my ancestor I would probably contact all cemeteries in Caldwell if you have not done so already.
Good luck in your search.