There's a brief passage about him in "The Right Stuff," noting him as successful yet accident-prone, which I found interesting. There should be plenty of primary documents about him but I haven't the slightest idea where to start even accessing them.
P.S. Would anyone else be interested in seeing more methodology threads?
A chapter about John R. C. Mitchell, USN appears in:
Colin Burgess, "Selecting the Mercury Seven: The Search for America's First Astronauts. Springer Science & Business Media, Aug 17, 2011" .... page 161.
Check the footnotes that correspond with page 161, and you should come up with a few of the leading documents regarding the retired captain.