"In the reorganization of the cavalry, Jackson, who had become a brigadier-general, commanded the Seventh and other Tennessee regiments; Colonel Griffith commanded the Texas brigade, composed of the Third, Sixth, and Ninth Cavalry; Col. Bob McCulloch, of the Second Missouri, commanded a brigade consisting of his own regiment and the First Mississippi."

I have not been able to identify the other Tennessee regiments with Jackson. It appears they were assigned to a position north of Holly Springs to prevent the enemies escape. Perhaps this explains the silence of their makeup.

It appears that DuPree's is the definitive work on the Holly Springs raid. Dunbar Rowland for one, sources him.

..........

"The new command began to assemble at Grenada about December 12. Its complement was about 3,500 men made up of Colonel Griffith's Texas Brigade, Colonel William Jackson's Tennessee Brigade and Colonel Robert M. McCullough's Missouri and Mississippi brigade."
Robert G.Hartje, Van Dorn, The Life and Times of a Confederate General, p. 255

Also sourced in a number of documents is Ross's Texas Brigade, Victor M. Rose,1881.