Suppose I have a regulated power supply that has +20V and -20V outputs, and an amplifier circuit that uses them. I also have a push-button (not momentary) power switch with an integrated LED which requires 12V to run. What is a simple way for me to adapt the existing PSU rails to also light the LED?
You can simply add a resistor in series with the LED. Either measure its current consumption, or assume that it's about 20mA. Then use Ohm's Law to work out a resistor to drop 8V (assuming it's connected from +20V to GND). Connect that resistor in series with the LED terminal of the switch.