This coil has a standard resistance/impedance

I see. I was under the impression that there’s a seperate resistor to avoid shorts when you connect from the trigger to ground.

What year/model of car?

It’s a 2014 Nissan Altima. I’ve spent quite a bit of time trying to find wiring diagrams, but I haven’t gotten very far. I got to the point I’m at now by following some old forum posts and confirming with a multimeter. What you described sounds accurate: the horn wire under the steering column seems to always be at 12v. Pressing the horn seems to send it to ~0V, so I assume it’s just jumping to the shared ground wire. I will say that when I disconnect to horn at the front of the car (to silence it), I can hear a relay in the engine bay clicking when I press the horn. I figure that implies it’s a physical relay, rather than a computer somewhere.

And realistically you could in a pinch pull coil power from the horn itself

This is something I’ve considered doing. The circuit I’m adding with the relay is extremely low current, so I don’t think it would be too tricky to run wires from a relay connected right next to the horn to the cabin. I can just ground the relay to the frame of the car right near the horn such that there’s minimal chance of creating a short on the high-amp horn circuit.