Mahlon, a J. G. Brawley was a private in the 36th AR Infantry. That is the only "J.-- Brawley" in an AR unit.

W. D. S. Cook was Lt. Col. 12th AR Infantry. I've never seen this unit referred to as a cavalry unit. This is the only field officer named "cook" or variation for an AR unit. A John B. Cocke was Colonel of the 39th (Hawthorne's, Cocke's) AR Inf.

Hope this helps.