On my yard dog I have the same set-up without the wire to the accessory terminal (I have no accessories), and mine works fine so the lack of that wire is not the problem. I don't understand how the tail lights got into the equation but I'd suspect that is the problem. Nothing should be feeding to the tail lights from the charging or ignition systems. I'd start by trying to find what is feeding them. They should be fed only from the light switch.
