Calvin Gilbert (no middle initial found) appears on the 1860 census schedule of Limestone County AL, age 24. He enlisted in Capt. Thomas J. McDonald's 9th Alabama Cavalry in the fall of 1863 but quickly deserted. Evidently Gilbert recruited his own company from the area around his home in Alabama and neighboring Giles County TN. This company joined a cavalry command being raised by Col. George H. Nixon (not found as Nixion) in the Tennessee Valley during the spring and summer of 1864. Capt. Gilbert signed his parole and a receipt as commander of Co. "E" at Courtland AL, June 20, 1864. He signed as regimental commander on Mar. 15, 1865.

Check here for more detail than you have about this regiment --
http://www.tngennet.org/civilwar/csacav/csa22bcav.html
During the Tennessee Campaign this cavalry regiment served as part of Col. Tyree H. Bell's Cavalry Brigade in Brig. Abram Buford's Division. There are many copies of the Confederate order of battle for Franklin available in print and on the web.
http://battleoffranklin.wordpress.com/2006/12/20/confederate-army-of-tennessee-general-john-bell-hood-commanding/

During the Battle of Franklin the divisions of Buford and Chalmers were taken away from General Forrest, so the only cavalry under his direct command at Franklin was "Red" Jackson's Division.

You could check the Alabama and Tennessee State Archives for any images of Capt. Gilbert or Col. Nixon.

Calvin Gilbert, born 12 January 1836, Giles County, TN; died 6 August 1885, Giles County, TN; buried Pleasant Hill, Giles County, TN; married 31 August 1858, Tranquilla Reed Gracey, born 15 October 1841, died 5 May 1925.
http://dutchforkchapter.org/html/gauntt.html