Roger wilco, I'll poke around in the other drain and see what comes out.
I just verified that turning the heat off stops the drip. Turning the heat back to full starts it again, about two drops/second. Turning the heat off again stops it.
Pretty definitely a compromised heater core, I would guess, draining through the same path that the AC evaporator would drain.
It probably had a rust leak plugged up with scale; the citric dissolved the scale and it's Katy bar the door. Drat.