I hunted for him, and my best guess is listed as J.I. Brooks, a captain listed as "slightly wounded" at Murfreesboro. He was part of the First Brigade, First Division of Polk's Corps. I guess it's possible that a slight wound could eventually lead to death in those days.
There's also a Capt. J.J. Brooks, which are his father's initials. A bunch of paperwork indicates Capt. J.J. Brooks, who was part of the 6th Regiment, Tenn. Vols., was seeking permission in 1861 to draw up his own regiment of infantry. And he was from Madison County, Tenn., which is the right area. The letters describe him as knowing the area well, etc. etc. But I can't find any followup to see if he actually did draw up such a regiment.