Indeed. The dying/screaming locust is trapped inside the horn relay itself. Jim's diagram in post #2 shows it as the contacts at the top of the picture. Those contacts vibrate like mad when voltage passes through. Terminal 4 carries the voltage, feeding it toward the ignition switch whenever key is in the ignition and doors are open. The ground for that circuit which actually triggers the noise is the drivers door jamb switch...that's why there's an extra terminal on the drivers door jamb switch with an insulator between the 2 terminals (if memory serves it's a black wire for buzzer, and white for the light? Maybe.), and there is only one terminal for lights on the passenger side jamb switch.
Should be easy to test your buzzer by applying 12V direct to terminal 1 (which is already done assuming your horn is functional), and then you simply jump from terminal 4 to ground. The moment 4 touches ground it should buzz if it's working. If it does, you're just missing continuity somewhere between terminal 4 and the door jamb switch...and most likely you'd lose that continuity at the ignition switch itself...OR you have the wrong door jamb switch installed/or 2nd wire is disconnected.
I discovered this whole stupid thing when I replaced my door jamb switch. I never knew the buzzer was there either. All of a sudden I replace the switch and eureka I have interior lights! Yay! And then I put the key in the ignition and I get this terrifying sound from under the hood which I never heard before. WTH?!!? I learned all this about 10 months ago, and it took me some exploring in my service manual to solve the mysterious noise and come to the conclusion it was entirely normal LOL, after finding that text and diagram that Jim posted in my service manual. Initially I was worried something really bad was happening electronically and that my horn was somehow getting partial voltage thru my ignition switch, but soon learned it was working exactly as designed!