No ..it's not normal. High resistance causes it and can leed to a meltdown.
First, I would check all electrical connections and make sure they are "set". If they are I would check each pin "to ground" with a meter... shouldn't be any reading. If that checks ok, then pull the harness and look for a burnt wire or overheated wire sheathing.

If you know what wire it is then disregard checking the wires. But check it to ground, etc,etc. etc..

ps..Another thing that should be done on an old car is pull the bulkhead connectors and look for corrosion. If they are original, they'll have (green)crud in it. I use Pepsi to clean the copper terminals. Pour some in a cup and dip the harness connector in it for about 10 minutes. Rinse off with water,dry and use a spray like WD40 or even white grease.