Anyone know what this wire is that I smoked?

Corrupt_Reverend said
It doesn't go through the firewall. It just goes from the resistor, across the engine bay, and ends at the cut on the passenger side behind the head.

It looks like someone added something on to that circuit at one time, and then it was removed later.

If that wire was just hanging by the firewall, then it may have shorted to cause the burnt wire.

I would just remove it from at the ballast resistor and keep the two original blue wires going into the ballast resistor.

That would be a good feed for an electric choke for a carb.