welcome to the garage Cuzzie, there's lots here with projects running endless years

for your question - no, the tail lights are on only when you pull the light switch out one click, key on or off - brake lights work regardless of the key position too, must be some wire wrong causing one or the other to get power from the key, they should both get power from the light switch .... have a manual? wiring diagram in it should show the setup, and there's a techtip about the sig stat wiring that might help, problem could be there
Bill