The whole rear passenger side tail light distorting to a melting

You have a short in the cross over wire. Almost all cars and trucks have one main break wire with a second wire "y" in off to the passenger side . You could just wire in a cross over and disconnect the old one.

That's very odd, because the wiring for all of the side markers are just splices from the nearest park lamp wires- the rear tail light in the rear (and the license plate lamps are also splices from these tail lights), and in the front side markers, they are splices from the nearest park lamps. Do all the other park lights work and turn on with the park light switch on? I would examine the 2 wires from that side marker's socket to the wiring harness it goes into-the power wire would somewhere splice into the passenger tail light wire. The other wire would be a ground wire and also splices into a ground wire for the rear end. To be on, the marker lamp would have to be getting power from some live source. I can't imagine where. Does the rear passenger light work correctly?

In that harness to the rear where the park lamps run, there might be a live wire going to an electrical trunk latch switch, or maybe a trunk lamp. If the wires were frayed right beside the side marker wire, you could have some cross feeding of power between the two. Let me know, we always appreciate feedback.

From inside the trunk remove the cover on either side & you will have access to the holdown bolts for the taillights (behind the lens)

Yes, I have a 2011 Milan as well and both sides of mine went out. One last year (2013) and the other side recently. My car is no longer under warranty and the dealer said they it would be $417 to repair. Ford needs to fix this issue because from what I have been reading it is a common problem and it is a safety issue!

Sounds like you have a melted tail light circuit board.

Made a video of me replacing the brake light but I show how to remove and install the tail light assembly. It's on a 2005 Hyundai Santa Fe but should be the same as a 2004.

check fuses with a tester. just because they look good can be missleading

Open up the hatch and look for the screws that hold the tail light assembly to the body. After removing them you can gently pull the whole tail light from the truck. You will seee the sockets that the bulbs are in and they twist like a bottle cap to get to the bulb. Just pull the bulb from the socket and reverse what you did to put it back together.

Bad earth connection.Clean or replce wire.

open the trunk remove the scuff plate that is located on the back part of the trunk closest to you. then pull the carpet back on the side that you are trying to get to and remove the three or four nuts holding the light assembley in. pull the assembley away from the body then disconnect the bulbs from the assembley. thay should just turn and come out socket and all.