HOT headlight Switch? Don't know why

1970 Dart 318 12v factory harness. We have been chasing this electrical problem for a while and for the life of us can not figure out why our LGN wire coming off the headlight switch to the foot dimmer switch is getting HOT. We have checked both the L3- 18R and L4- 16V* from the headlights to see if they had a short to ground and they are not, unless we have the headlights plugged in. Which I believe is correct because it runs thru the headlight to the ground? We replaced both the headlight switch and foot dimmer switch with no positive result, we still get a very hot LGN wire at the headlight switch and the foot dimmer. We ran a jumper from the battery to the H connector on the under dash harness which is the LGN wire to eliminate the headlight switch and other wires in that connector and the LGN wire from the headlight switch to the foot dimmer is still getting hot, as if it was going to ground.

We have rung out the wires from the headlights to the bulkhead connector and checked to see if they were grounded and they do not seem to be grounded. We have checked the LGN wire to ground and there is nothing unless the headlights are plugged in.

Not sure why this wire is getting hot, it got so hot it melted the headlight switch. This is what started this hair pulling adventure.

Any help or direction on where keep looking would be a huge help.