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Here is a card I happened to get in the mail today of Oliver Wendell Tebeau who became manager of the Cleveland Infants in 1890 at the age of 25. He continued as a player/manager through 1898 with the then Cleveland Spiders.
Jack McGeachy was 24 with Indy in 1887 when Burnham left his post as manager. I have not been able to find any indication that McGeachy managed Indy, but he appears to have been an established starting player at 24 and may have been player manager for a brief interim period.
After learning about the Detroit and Indy combined photoshoots it seems more likely to me that the resulting McCreachy card was some sort of mix up, rather than an elaborate riddle.