I'd check around Tarrant County. There was a "Gilmore's Guards, Mtd Inf Tarr Co 20th Brig TM." mentioned at http://www.rootsweb.ancestry.com/~txtarran/military/robert-e-lee5.htm and "John R. Brinkley served 5 July 1861 in Gilmore Guards, Mounted Infantry, Tarrant County, Texas. In 1863 he served in Company H, 2nd Cavalry Regiment, Texas State Troops, Tarrant County, Texas" mentioned at http://familytreemaker.genealogy.com/users/b/a/t/Margaret-R-Bates/GENE15-0054.html. Perhaps Seaborne Gilmore or a relative (Mexican War veteran who was Tarrant County's first elected county judge--see http://www.rootsweb.ancestry.com/~txtarran/historical14.htm).

That's just speculation.

Vicki Betts