Also got the impression from this image that he is wearing postwar fashion. But will focus on the 'JCB' badge shown on the kepi, as the sole clue.
If the choice is between whether 'JCB' stands for either 'John Cabell Breckinridge' or 'John Calvin Brown', would opt for it more likely being Breckinridge here.
Reasons: If Gates enlisted in '61 in the 6th TN aged 18 years (or older), he would have been aged around 30 years (or older) when Brown became TN Governor in 1871. But the young lad wearing the badge in this picture looks to be aged barely 20 years, if that. This would support the claim that the photograph was taken in '61, shortly after Breckinridge campaigned for the Presidency. (Further, prior to Gates being captured in '64, don't believe the 6th TN ever served in a brigade or division led by Brown so that any connection could be established on this basis).