Dear Ms. Daviss-Mitchell,
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 search for a record of J.P. Taylor’s birth in the FamilySearch index for Texas Births and Christenings, 1840-1981, request a birth record search from the Harrison County Clerk, and review the FamilySearch Research wiki for Harrison County, Texas Genealogy.
We hope this is helpful. Best of luck with your research!