no it wouldnt melt, just last week i had the same odd issue with the tach, jumping mainly at 3k+. the computer threw a code 42, for ignition module, so i changed it, still no good, i then swapped in a diffeent dizzy, still no good, then i used a flowchart for troubleshooting code 42 and turned out to be the est wire grounding out. I had used a small piece of a coat hanger to hold a bunch of wires together about the height of thew valve cover on the pass side, but the heat apparently made the wire melt into the est wire, and when running the whole wire bunch would move around and the est wire would ground out through the coat hanger wire into the back lip of the valve cover, it was such a freak thing, but i pulled the hanger wire off and taped it up and its 100% fine now. Maybe not the exact thign in your situation but worth checking out.
chekc this out, the part that may help you is where it says probe the tan/black wire with a test light and 12v. thatll show if theres a short. This is for a 86-89 tpi car but wire colors were the same for my 90-92 setup just different terminal locations, but the white wire and tan/black should be found on yours as well.
http://www.chevythunder.com/est_code_42.htm