Could these 2 problems be related somehow? The regulator melted and dripped down the fire wall. The ballast resistor is ridiculously HOT. Now and then the engine cuts out while driving down the road or just idling in the garage. 71 Charger with electronic ignition conversion.

Possibly, did you do anything electrical recently?

Ballast resistors get hot, burn your fingers hot, normally.

Isolated or “dual field” alternator? I’m not too familiar with non-68s, I think the field wiring and ignition 1 wiring are on the same circuit coming out of the switch. But it is odd for two branches to meltdown

I have done nothing recently. I have a 76 Cordoba sitting right next to it and its resistor is no more than warm. I bypassed the Lean Burn on that. Right next to the Cordoba is an 80 Mirada its ballast was hot also. [censored]? Not sure about the alternator. How do I tell?

It's normal for ballast resistors to get hot. I don't know if another problem can make them get hotter then normal but it's caused by the way they work.

I've never seen a regulator drip it's goo but the ECMs do that with age.

What was condition of wires to regulator?
Any indications of excessive current draw?
Ballast typically just "burn open" but don't short.
But a regulator can have a short internally.

The wires look fine. No indication of anything out of the ordinary.

The reg. in my truck melted down the firewall and all over the bellhousing years ago but its never gave me an once of trouble....knock on wood.

I'm not sure it actually melted I have components in a box, not even in use, that "melted"

Yes, the potting material degraded. It happens, not due to heat so much as old age.

On stock configuration there is no a straight relationship between Ballast and reg, more than just share the same input signal source from Ign switch, but nothing going throught between them.

JUST cranking the Voltage reg can get load coming from ballast by the default on the Chrysler dual circuit ign system design, but that's just for that instant.