Terry,
Get a copy of the regimental history of the 13th Tennessee by Alfred Vaughan. It has been reprinted and should be able to be found on line pretty cheap. It is thin and is a quick read. Also check Lindsley's Military Annals for a brief history of the regiment. There was a John T. Gregory on Company D of the 13th.

The 13th Tennessee was an outstanding unit, and fought in some of the tightest spots in some of the toughest battles in the Western theater. For example, at Chickamauga the 13th was in action at Brock Field, and were in the night attack that captured the 77th Pennsylvania where General Preston Smith was killed. At Missionary Ridge, they were one of the units that delayed the Union advance after Deas' brigade broke and were sent to reinforce the 11th Tennessee in a fierce but unsuccessful counterattack to drive the Feds off the ridge. At the "Dead Angle" at Kennesaw Mountain, they were posted just down the line from "the angle." At Franklin, they were one of the few units that actually penetrated the Federal inner-line on the Columbia Pike there at the Carter House.

If you have any specific questions on the 13th, send me an e-mail, I might be able to help.