You must be thinking about Elijah V. Mullinax of Co. "H", Ramsay's 1st Georgia Regiment, who enlisted at Dahlongea GA, March 18, 1861, for twelve months. His command entered Confederate service at Pensacola FL on Apr. 16, 1861. George W. Mullinax did not enlist until July 24, 1861, by which time the regiment had been in Virginia for some time.

I don't see later service for E. V. Mullinax. However, George W. Mullinax reenlisted for three years or the war on Mar. 4, 1862, joining newly formed Co. "G", 39th Georgia Regiment at Camp McDonald GA. Also joining the same company were Francis M. and William R. Mullinax. W. R. Mullinax died on Apr. 19, 1862, shortly after the regiment left camp

Probate papers filed in Gilmer County GA are found in the service file for George W. Mullinax, Co. "G", 39th Georgia Regiment. These state that G. W. Mullinax died at Chattanooga TN, Apr. 25, 1862. Papers were filed in behalf of the widow Rebecca Mullinax, who married G. W. Mullinax on Sept. 8, 1861. After the war she apparently filed for pension benefits in her late husband's name.

Copies of all the files mentioned are available here.