I had the headlights and other items go out on my 2005 convertible. Pulled the interior trim and pulled the plug off of the switch and sure enough the same positive connector is melted. I bought a new switch at Advance Auto Parts for $46 and will try the new switch out soon. This thread is a lifesaver! I had randomly smelled burning wires in the car a couple times over the weeks prior to the main failure, so I hope this is the fix. If it happens again I will need to figure out how to rewire the headlights through a relay or something.