I don't think it was ever stated where Auxiliary Control (I assume that was TOS's equivalent to the "Battle Bridge") was located. Since it's been proposed that the saucer could be separated on the TOS Enterprise as well, I surmise that Aux. Control on the TOS E was similarly located in the secondary hull, probably near the Engine Room. (Odd to call that section "Main" Engineering in light of the fact that few if any sets were ever shown that could be considered auxiliaries of that section.) And yes, it's safe to assume that every Starfleet ship has an Auxiliary Control, though it's not clear why it's so seldom used.
"Now I did a job -- and got nothin' but trouble since I did it, not to mention more than a few unkind words as regard to my character, so let me make this abundantly clear: I do the job... and then I get paid. Go run your little world."