I had the connector for the headlamp melt (but not cause a short) on my 95 SS. A replacement can be found at Pep Boys for $2.95. Comes with enough wire length to allow easy splicing into the old wires.
If that isn't your source of the short, you will need to start looking at every connection for possible corrosion. I recommend using some sort of dielectric grease or spray on the connectors to keep water out, and corrosion from forming again. After cleaning the existing connections of course.
I've done this to my 01 SS 900ie, and sprayed every connection with DeoxIT Gold.
http://store.caig.com/s.nl/sc.1/.f
Good preventative maintenance (recommended by LT Snyder too...)
bill