66 Dart 270 Brake light fuse heats up??

What gets my attention is the fact that there is no fault before headlights are pulled on. If yours is like most, you have 1 fuse that isn't hot either end before park lamps are pulled on. The headlight switch energizes this fuse and the park lamps. So lets remove this fuse, pull the headlights on and see what happens. The headlights would still work but park lamps, illumination ( orange wires ) would not. If the brake lamp fuse doesn't heat up we know there's a fault in the park lamp circuit. How/where it effects the brake lamp circuit/fuse is still a mystery ( rear lamp bulbs and sockets would be suspect ).
I am assuming everything else works as it should. If the dome lamp, some indicator in the inst' panel, license plate lamp, anything doesn't work as it should... we need that detail/clue.