Can someone identify this for me?

I don't know about a "Headlights On" buzzer, but I had a 70 Fury with a factory "Headlight delay" option. If you turn the headlights off after you shut the car off, they would stay on for 30 seconds or so then go out. I found this out by accident & didn't know it was even available in 1970. So maybe that's what that thing is? Your car could have that option, check that out.