Nope, it only sounded when I had the headlight
disconnected or when it was off the bike and tested straight to the battery. I pulled the headlight wiring today, just as it was when I forgot to wire it yesterday, and it didn't sound in either of the two on positions...confounding! So I pulled the harness from the headlight bucket to the horn/light switch and redid some electrical taping, but there was nothing else weird happening with the harness. All contacts have been sprayed and cleaned.
As I was mucking around with it today, I noticed the neutral light dimming as I was pressing the horn button. I've got the battery on a charger overnight, hoping that it just needs a good, solid charge to keep that horn working. Kind of a stretch, but we'll see tomorrow morning. I'm fixing this goddamn horn tomorrow, all day if necessary