Dear Sir,
There was a 12th (Day's) Tennessee Cavalry Battalion and 12th (Richardson's-Green's) Tennessee Cavalry Regiment. These are two different units. 12th (Day's) Tennessee Cavalry Battalion was organized 1 September 1862 and consolidated with 16th Battalion. The combined organization was known as Rucker's Legion and I know fought at Philadelphia, Tennessee on 20 October 1863. 12th (Richardson's-Green's) Tennessee Cavalry Regiment was organized on 14 February 1863 within Federal lines and reorganized 4 February 1864.
You can find short histories for these units in "Tennesseeans in the Civil War", Part 1, pages 33-35, and 80-82 respectively. These pages do give you some information on the counties of origin. Just glancing at the histories I can not see a reference to residences of Kentucky, however, it may be a case like often happened along the Tennessee/Georgia state line when relatives joined the companies/regiments of a neighboring county in another state to be with relatives.
I hope this helps.
Respectfully,
Gerald D. Hodge, Jr.
Niota, Tennessee
War Between the States Historian
Historian: 39th Georgia Infantry Regiment
Web Master: http://39thGAVOLINFRGT.homestead.com/39thHomepage.html