Ms. Eells, I have recently started researching Elisha and Emily Brown in hopes of solving my own brick wall on Browns. According to the death certificate of Elija Patrick Brown (who died 1928 in Anarene, Archer Co., TX), his parents were Elisha K. Brown and Emily Sanford. The death record also states that Elisha, his father, was born in Lebernon, TN (which I presume is Lebanon, TN). There was no town given for Emily, just TN. The information on the certificate I believe was given by his son John A. Brown. There are Brown families on early tax lists for Wilson Co. but that is as far as I have got.
Do you have any information on the other children of Elisha and Emily? I am trying to research my great-grandfather James Madison Brown who was from the Madison Co, TN area. He lived in Jack Co, TX (adjacent to Archer Co.) and had a neighbor or theorized brother named Balaam or Balyum T. Brown (whose wife was a Sanford) and both have birth years that seem to agree with the censuses you have found. James' children's names are all very similar to the names of children of Elisha and Emily though in a different birth order. Seems to be a good connection (though I have had many false leads before).
The death certificate I spoke of can be viewed on familysearch.org and you can find Elija P. and wife on findagrave.com. I have also found online the wife's obituary. They had a son John A. and grandson Elmer.