The Arkansas pension application of C. C. Tate claimed service in Co. K, McNeil's Arkansas Infantry, 1863-1865.
Col. John McNeil, of Clark County, commanded McNeil's Arkansas Reserve Infantry (not to be confused with Col. Archibald J. McNeill, who commanded McNeill's 30th Arkansas Infantry). I know nothing about this regiment, except to say that it was apparently organized in 1863, and consisted of ten companies from southwest Arkansas.
Hopefully, someone more knowledge than I will pitch in and expand on this obscure regiment.