Here's the book you want to try to find. You may need to use inter library loan to get it. "Histories of the several regiments and battalions from North Carolina in the Great War 1861 - '65," by Walter Clark. Published about 1901 by the state. A corporal Rose of the 24th wrote an entry on the 24th, pages 269 to 290 of that book.
You can also look for the North Carolina Adjutant General's Report. If you know the county your ancestor came from, check for a historical society. Also look for period newspapers from that area. National Battlefield Parks have archives, many contain letters and diaries from men who fought there. Check out battles that the 24th fought in.
Check the North Carolina Department of Cultural Resources, Division of Archives and History, at Raleigh, as well as the State Library in Raleigh.
Hope this is of some help.
Regards, Dave Gorski