Well, I must say, you could hardly have picked a more difficult person to track down, though it would help if you gave us more information; a state of origin, perhaps? I have potential "James Mills'" from eight different states, "James S. Mills'" from three, and "James Spencer Mills" from none; however, if the two James Spencer Mills' who I can find who lived within that specific time frame are useful in narrowing down my focus, I think it is safe to discard the Pennsylvania reverend and concentrate on the South Carolinian, in which case, there are only a few possibilities; the most likely is a "James S. Mills" who served in Stalling's 8th SC Reserve Battalion, mustered into state service in July of 1864 and Confederate service on 31 October 1864. This is where it all sort of breaks down, unfortunately; several heavily-depleted regiments and battalions in Johnston's Army of the Tennessee and in the Department of South Carolina, Georgia, and Florida (both of which Hardee's Corps served in during this time period) were consolidated to form slightly stronger ones, and the consolidation records are a bit contradictory; the unit is recorded has having variously been disbanded in February of 1865, consolidated with different units at two different times, or being mounted and transferred to Wheeler's Cavalry, and I'm not even entirely certain whether it ever served under Hardee or not; assuming I'm dealing with the right James Mills here (which, as I said, more information would be appreciated), I can try to sort all that out in the next couple of days.
If we are dealing with the right person, there are two other "James Mills" entries (sans the "S.") that could also be him, as they both serve in short-term units with non-overlapping terms-of-service earlier in the war, the 90-day 11th SC Reserve Regiment in the winter of 1862-1863, and the 6-moth 2nd SC State Troops in 1863-1864. It is not out of the realm of possibility that all three of these entries are for the same man. Again, I can try to sort that out in the next couple of days. I am, however, inclined towards skepticism in these earlier two cases, since, with the dates given, Mills would have only been 14 at the time of first enlistment. In the case of the 8th Battalion, however, his age of 16 would not have been at all rare, and the roster for Captain Fishburne's Company B (in which Mills, James S. appears) has dates-of-birth for some of its privates, and many are quite near that age. This was far more common in the waning months of the war; at Bentonville, at which the 8th may have served, one of Hoke's Brigades was a reserve unit consisting almost entirely of teenage North Carolinians.