Voltage regulator smoking?

Yeh you for sure have a problem on your hands. if things get too bad on the bulkhead connector, and you are not terribly fussy about "restoraton accuracy," you could pull the bad wires loose, either splice to them for slack, or if you can generate slack, pull the terminals out of the connector, snake the wires through the connector and just semi permanently splice the two together. Way way back in the '70's my 70 RR ate up the connector where the ammeter wires went through. I just reamed out the connector body with a drill, snaked wires clear through the connector, and connected them up.

I believe I said before, judging from what we can see, things have been warm. Be particularly aware, that wires wrapped together can "cook" in the wrap, and melt insulation, melt wires together and form unwanted shorts/ crosses between wires. THAT can be a nightmare to find, in a hidden, hard to reach section of harness