Hi, CM. You're probably not seeing it because it's so simple.
Let's ignore the "To IGN-AUX" part of the circuit (which happens when it's at 0v, i.e. the ignition and aux are off, and the diode prevents current from flowing). The buzzer BZ1 is a low current device. When "To Lights" is high (i.e. the lights are ON), 0.7V will be dropped across the diode, and a volt or four across the 1K resistor, leaving 8 to 11 volts across the buzzer, enough voltage to make the buzzer sound.
Now let's assume the key is in the ignition and it's turned to AUX or ON. There's 12V there, so 0.7V will be dropped across the diode, and the rest will be dropped across the 1K resistor. That means there will be no voltage for the buzzer, and it won't turn on.
Net effect: the buzzer will only turn ON when the IGN/AUX switch is OFF and the lights are ON. Simple & straightforward.
A buzzer isn't specified. I'd recommend trying your buzzer or binger with 12V and a 1K series resistor before you install. It's possible it might not be loud enough for you.
Good luck Chris