Heat = bad connection = voltage drop. You need to clean, or replace the brass connectors to eliminate this added resistance. Chances are good that other connections in your bulkhead connector are deteriorating as well. This is normal Chrysler wire harness aging, and causes all sorts of electrical problems.
You don’t have to bypass this connection, just clean it by removing the white or green corrosion, and apply some dielectric grease. Or if you have the ability to change out the male & female brass with new replacements that would be best.