Smoked HEI coil.

I have never seen a coil of any kind not draw current with the key in run.
I worked for GM for 15 years and the biggest coil killer was poor quality plug wires, so maybe it was on it's way out and the key on killed it.

I don't know why you did not notice this. I'm telling you, a genuine GM HEI does not draw current with the engine stopped. I noticed this when doing my first conversion, a Toyota 20R with factory distributor firing an HEI 4 pin installed in a Cletrac dozer. When I wired up the 67, same thing. It may be that not all replacement aftermarket modules do this.