Lyn -
Tail lights, running lights, brake lights, are all powered from the tow vehicle. No trailer battery necessary.
All interior living-space lights - ceiling lights, etc - are powered from the TM battery.
If you have one brake light that works, an one that doesn't, the problem is almost certainly in the bad side's brake-light socket. Assuming the bulb is good, then either the button contact in the socket is corroded, or the ground wire right there in the socket is corroded. Disconnect the TM from the tow vehicle, open up the tail-light fixture, and rummage around. I bet you'll find it.
Bill
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