Apparently the 8th Tennessee Cavalry and 13th Cavalry were one and the same, how the two designations came about I cannot say.
A 30 page write up on the 8th will be found in "Military Annals of Tennessee, Confederate," Edited by John Berrien Lindsley, Broadfoot Publishing Co., Wilington, NC, 1995, originally prited 1886, frequently called "Lindsley's Annals" Pages 673/4 note two engagements in which Capt. Gore lead the regiment in action.
Mounce L. Gore originally served as Captain, Co. G., 8th Tennessee Cavalry, and was promoted Col. of the 8th the last of March 1865. Tennesseans in the CW, Part 2, list him as Col., 13th Tennessee Cavalry.
The fellow at this address apparently has more information on this unit:
13th (8th) Tenn. Cavalry 74160.2703@compuserve.com
At Sparta, Tenn., in September, 1883, General Dibrell's old cavalry command organized a brothood, officered with members of his old regiment, the Eight Tenneessee. At their second meeting, held at Gainsboro in 1884, the following commands were added to the organization . . . General Dibrell commanded this "reunion brigade" up to his death in 1886. [Confederate Military History, Vol. VIII, Edited by Gen.,Clement A. Evans, p. 307]
The U. S. Army Military History Institute at the Carlisle Barracks, Carlisle, PA list the following for the 13th:
USAMHI
RefBranch
laf Dec 90
13th Tennessee Cavalry
Confederate Military History, Extended Edition. Vol. 10: Tennessee. Wilmington, NC: Broadfoot,
1987. 806 p. E484C65.1987v10. (Contains numerous, scattered references to Tennessee units).
Crute, Joseph H., Jr. Units of the Confederate States Army. Midlothian, VA: Derwent Books,
1987. Ref.
See pp. 287-88 (2 photocopied pages) for a concise summary of the regiment's service.
Sifakis, Stewart. Compendium of the Confederate Armies: Tennessee. NY: Facts on File, 1992.
pp. 62-64 (2 photocopied pages). E579S53.1992. (Unit organizational history).
Tennessee. CW Centennial Comm. Tennesseans in the Civil War: A Military History of Union and
Confederate Units.... Vol. 1. Nashville, TN: By the Comm, 1964. pp. 83-85 (3 photo-copied pages). E579.4A53v1. (Brief unit history).
The following pertinent personal papers are in the Institute's Manuscript Archive:
Ray, James K. P. - CWTIColl
Good Hunting,
George Martin
Sparks, NV