You obviously have a pretty bad electrical issue as I have read some of your other posts and many issues are coming to surface with your truck. I believe you said that you already replaced your headlight switch, was this with a new one or a junk yard one? Next thing to look at is the wiring harness leading up to the switch. As stated, the supply wire to the switch is small and heat will take its toll on things over a twenty some year span.
You stated previously that you are not too savvy at electrical issues. Thats ok, you are at the right place for help. Get a good wire stripper and crimper from an electrical supply store or the electrical section at your local Depot or Lowes.
http://www.homedepot.com/h_d1/N-5yc...eyword=wire+stripper+crimper&storeId=10051The chinese cheapies suck and will disappoint you.
Next you need some wire. Most of the ones supplying your switch are 18 gauge which will require red crimp splices. Blue are for 14 and 16 gauge wire, bigger than #18 wire. Yellow ones are for 10 and 12 gauge wire. I got a fishing caddy and filled it with a large stock of various crimp connections, real handy.
Find your section of melted wires and cut out the damaged section. Cut new wires and splice them in to repair your harness.
Do some research on relays.
http://napaonline.com/Catalog/CatalogItemDetail.aspx?R=ECHAR143_0252370213 You can use them to cut the amount of power going through your headlight switch so this issue does not happen again. There are even pre made harnesses to make installs easier and neater.
http://napaonline.com/Catalog/CatalogItemDetail.aspx?R=ECHEC23_0215193739 Search this forum for the headlight relay mod. Your lights will be brighter and your switch will be cooler. Buy a cheap multi meter and keep it handy. You can check for voltage and use the resistance portion to check for bad wires, light bulbs, and many other things. Seeing the voltage drop from your battery to your lights will give you a new respect for how electrical circuits work. I had 12.5 volts at my battery with the engine off and 7.7 volts at my reverse lights. After a relay mod, the voltage jumped to 11.5. My reverse lights now look amazingly brighter when I look in the rear view at night.
Don't be afraid to dig in and don't be afraid to ask questions and post pics. Good luck dude.
Now get busy.