The disk you have is piezoelectric crystal disk on a thin, wider brass disk.
The crystal disk Diameter shrinks when charged, making the brass disk bend/dish.
The more V across the wires, the more the crystal disk shrinks and brass disk bends.
I squeeze the disk, the 2 wires act like a charged capacitor. When I release the disk, the flow reverses. Just tapping a piezo makes enough energy to flash a led.
Each disk wire needs 2 diodes. 1 lets current flow from GND to the disk and the other lets current out as signal. Press will signal on one wire, release signals on the other.
I find that bipolar junction diodes, leds and transistors tame piezo spikes even when smacked hard with a screwdriver handle... short of shattering the crystal which yeah done that once out of 10 bags of 10.