You did not list a unit I found at least 3 possible men in the Civil war Soldiers and Sailors System---

Garrett, Thomas J.
Side: Confederacy
Location: Alabama
Battle Unit: 12th Regiment, Alabama Infantry
Function: Infantry

Garrett, Thomas J.
Side: Confederacy
Location: Alabama
Battle Unit: 17th Regiment, Alabama Infantry
Function: Infantry

Garrett, T.J.
Side: Confederacy
Location: Alabama
Battle Unit: Hilliard's Legion, Alabama Volunteers
Alternate Name: Thomas G./Garrett

From what I gather, Camp Davis was in Georgia----https://www.effinghamherald.net/local/around-town/history-comes-back-to-life-at-camp-davis/

https://woodlawnplantation.com/history/

Also this variation---
Garritt, Thomas J.