Piezo buzzers are self oscillating... So you can directly connect it in your circuit, but you may have to connect any voltage regulator or resistor divider to reduce voltage from 36 to 12. You no need to add noise to produce sound. But you know your circuit, you have to connect it accordingly...
When the battery is connected at reverse polarity...
It has the effect of reducing all voltage drops in the loop. You may have trouble finding a sufficient supply voltage to drive a piezo beeper.
What will also happen is current will go way up. Therefore if you can find some resistive component in the loop, it may develop sufficient voltage to drive a beeper.
you connect the battery only through a series Diode. After the diode on the battery side connect the buzzer with a diode in series . ie connect the anode of buzzer diode to -ve. accross the buzzer you can put an LED with a series resistor. Hope your problem is solved if so dont forget to click the helped me button below