No,the 13th Infantry was not a "Buffalo Soldier unit".
However as Lt Parker notes in his recounting "During this last engagement it had been necessary to obtain more men
to assist in carrying ammunition, and Capt. Ayers, of the 10th Cavalry, had furnished a detail, consisting of Serg. Graham and Privates Smith and Taylor, Troop E, 10th Cavalry."
Lt Parker states "These colored soldiers proved to be excellent. They remained with the battery until the end of the fighting on the 17th, and were in every respect the peers of any soldier in the detachment. Serg. Graham was recommended for a medal of honor. Privates Smith and Taylor did as good service,were as willing, as obedient, as prompt, and as energetic in the discharge of their duties as any commanding officer could wish to have."
Lt Parker adds "It is a great pleasure to be able to give this testimony to the merits of our colored troopers, and to say, in addition, that no soldiers ever fought better than the "Brunettes" of the 9th and 10th Cavalry, who fought from the 3d of July until the 12th, near or with
the Gatlings."
Thanks for your reply, ijcr. How did you find this gem?