running lights not working

the tag lights, tail lights, marker lights, gauge cluster lights, radio backlight and heat/ac backlight all stopped working at once on my 83 TC. head lights and brake lights still work. the only common point that i know of for all these lights is the rotating dimmer switch that turns on all the lights. i bought a new switch but when i went to swap it in, i noticed that the plug that goes into it is slightly burned in one corner. does anyone know what caused this and if there is an affordable way to fix it?