Wow, really getting some great information from everyone. Learning more than just how to fix this problem but also some historical things as well.
I'm out of town for the week but right before I left I cleaned up the ignition coil and cleaned the connections going to positive and negative. The resistor wire is the cloth covered wired correct? Attached is an image. The wire didn't look like it was in great condition as you can see. I want to trace the wire as I feel like the work the mechanic did on the gas gauge might have been what created this.
At any rate, stand by for more updates next weekend.
The new guy
'63 GMC 305, 4 on the floor - farmer Frankenstein edition