69 ignition problem???

Next challenge. Take a look at the photo of the bulk head plug. Now what? Solder the wires? Replace the bulkhead plug??

I am open to any and all suggestions.
Describe your bypass/jumper.

The question I still have is why did that connection get so hot.
The one below it with extra insulation is probably the alternator output, and that does not show external signs of overheating.
I'm not sure you're quite done troubleshooting.

The wire that's overheated is the ignition wire, not the alternator feed (heavy black). Don't see how MAD's pitch is relevant. Look at the condition of the battery feed/charging terminal. That's the blue fusible link going into the connector. If its not showing signs of overheating, then its not been overloaded. Clean and lets find the cause of the ignition connection overheating.

The '69 Dodge Service manual shows the ignition feed (J2) goes first to the voltage regulator, then the ballast resistor (J2A).
First thing is to confirm if that's true.
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It's possible that the cause was simply that the terminal connection was poorly made.
But keep in mind the normal current loads on the circuit.
There's only two items that draw power through J2; the alternator's rotor, and the ignition coil. Stock alternator and ignition this will be around 5 amps maximum.
Since its running, maybe do a quick check that the regulator isn't full fielding. You see this as overcharging on the ammeter and voltage that increases with rpm beyond the normal range. (above 14.9 V)

There may be other things to check, based on the initial description of the ignition switch working when in a halfway position. That's why I asked about the jumper.