Since you know when and where Eurastus died, obtain a copy of his death certificate. It should have the names and birth locations (state/country) of his parents - this would give you the maiden name of his mother.
I see a Mrs. E.W. Smith of Bexar Co, TX receives an Confederate pension in TX. There are not a lot of men's given names beginning with letter "E", you might want to check that out. If the forms and questions were anything like Alabama's, you might find quite a bit on her, and Eurastus.
You might want to check Bexar Co, TX GenWeb site, some GenWeb counties are putting their cemeteries online. Post a query there, and on the Burleson Co, TX GenWeb site, too. And, if you haven't already done so, post queries on the GenForum sites for those counties.