Got new connectors from the junkyard and was able to swap them in to fix the wiring. Now the blinkers work properly and so do the windshield wipers.
Above is a picture of the ignition switch connectors. Notice the cracks and deformation of the one with the wires in it. When I moved them over to the other connector I had to break it to get two of the wires out. This is what can be a nightmare for someone because if the connector gets melted to the point where a positive and negative wire arc or make contact it can start a fire. The car doesn’t have to be running for that to happen.