Ellender J. "Ellen" Taunton (correct spelling) was Henry Gaither's second wife. He first married Missouri Britton (b. c1837) on 28 Sep 1858 in Tallapoosa Co., AL. They had one child, Ann Amanda Adeline Gaither (b. 10 June 1859), who went on to marry David Clopton Taunton, a nephew of Ellender J. Taunton. Henry was listed by himself as a boarder in a hotel in Tallapoosa Co. in the 1860 census, and his wife Missouri and daughter Amanda were living in Coosa Co., AL in the household of Missouri's mother, Adeline Britton. In 1870 and 1880, Henry and second wife Ellender were living in Elmore Co., AL.
Considering the use of the names Greenberry, Eli and Georgia among Henry Gaither's children, I'd bet that he's connected to the Greenberry Gaither (b. c1793) listed in Coosa Co., AL in 1850, especially since Henry's wife Missouri was also living in Coosa Co. in 1860. This Greenberry Gaither had wife Ann (b. c1799) and children Ella, Sarah Ann, Mary P., Eli, Richard, and Georgia M. Henry Gaither listed his birthplace as GA in his census entries, and this Greenberry Gaither, his wife, and all their children (with the exception of Georgia) listed their birthplaces as Georgia as well. Coosa Co. is wedged in next to both Elmore and Tallapoosa Cos., where Henry is later found.
I'd suggest looking at the Coosa Co., AL records to see if you can find any connection between Greenberry and Henry. The ages would be right for Greenberry to be Henry's father; perhaps a will or probate/estate record would confirm this.