If you have time, you may wish to look through the Galveston and Houston Newspapers of the period for information. Especially if you think this soldier might have died because this kind of information occasionally appears in the newspaper. You might also want to consult the cemetery records for Galveston or Robertsopn County.
BTW, The town of enlistment mentioned is Owensville which is about 3 miles north of Franklin, Robertson County, Texas. Nothing remains of Owensville, but there is a Texas Historical Marker, See link below:
http://www.civilwaralbum.com/misc18/owensville1.htm
Best wishes,
W. Bozic