Electronic – Creating a momentary low pulse with a toggle switch

Here's another alternative with two inverters and debouncing:

For logic output, only the two inverters, RC, and feedback resistor are needed:

NC7WZ14 is $0.06 with 2 inverters, small 6-pin package, and Schmitt trigger inputs, though I think this circuit doesn't even need Schmitt inputs because of the RC. Also it can drive 24 mA, so you could connect the LED directly to it if you're using an LED for whatever reason.

Also shown here and here as a toggle touch switch.

I think the feedback resistor has to be much smaller than the center resistor to prevent it from oscillating if you hold down the button, because the low-impedance connection to the output will prevent the capacitor from charging to the middle voltage until you let go.

Variants are described at Press ON - Press OFF soft latching circuits:

Believe it or not, that black lump is epoxy covering an integrated circuit, probably a small microprocessor. These are often caseless chips, just the IC die glued to the PCB with fine wires between the pads on the chip and PCB.

Many microcontrollers can be put into a deep-sleep state where they draw just a few microamps, so little so as not to significantly affect battery life. They spend all of their time in deep sleep until someone presses the button, which is connected to an interrupt line to wake it up.