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First, the Colonel was Galusha Pennypacker, not Pennybacker. Second, I don't understand why you bring the Colonel into your search, as he was not with the US 16th Regular Army until shortly after July, 1866, when he left the US 34th Regular Army. During the CW, he was in the Pennsylvania 9th and 87th Infantries. He would not have served at the same time as your ancestor.
As for John C.White, I see him listed as a musician in the US 16th Regular Army. I also found a record for a John C.White in the US Army 1st Dragoons, Companies E & I. Is it possible he served this unit, then later the 16th, or are these different men?