Not sure which pickup you have, I was thinking the newer one, but rockauto shows that and the older one as well. Does the pick up have a round connector or a flat one with two prongs?
As for unplugging the CTS theory, I dunno. It locks out the advance so you can set the timing but other than that I have no idea what it would do. Have you tried it?
They say there are no such thing as a stupid question. They say there is always the exception that proves the rule. Don't be the exception.