Do you mean a stand-alone pedal? Battery or One-Spot power for the internal workings can also light an LED.
Or do you mean a remote-control for an amplifier?
It is perfectly possible to feed power down and detect how much is eaten, use that fact to control switching.
Simplest case: Find 14V DC inside the amp. Feed this through a 12V 20mA relay coil, to jack to pedal. Inside the pedal a switch opens or closes the path through (~~2V) LED and back to amp power common.
Switch on: both LED and relay are "on". Switch off: no current flows, both LED and relay are inactive.
Well, if you do that much, the buyers want more. For two switches and LEDs, one way is to feed AC to the pedal. Diodes split the path + to A and - to B switch/LED. Inside the amp something clever splits + to A relay and - to B relay. However half-wave AC to relays is ugly stuff. Also it isn't always convenient to get voltages and currents in LEDs and relays in the same ballpark. Usually some chips are used to buffer and steady the drive to the relays.
OTOH, with a TRS plug you can have two discrete paths, and use the simple scheme twice. The product Jaz pointed to shows a typical pedal schematic, except the logic is reversed. If fed 14V through 680r resistor, the Tip contact is 14V when LED is "off", 2V when LED is "on". You could reverse the contacts of the relay to get the effect state back in sync with the LED state. They probably put more (and more) stuff behind the amp jack to work the relay indirectly.
2-switch pedals are an old standard. How do you get buyers to say "WOW!"? I was just looking at (and head-scratching over) a Mesa plan with 5 or 6 switches and according LEDs. It did use a many-pin DIN plug instead of simple 1/4" plug. They seem to have come to it round-about. Power to pedal was +2V and -3V DC derived from heater winding. There were logic chips inside the pedal, and a MML DAC. The amp had a bar-graph chip, plus some different MML logic in a variety of discrete devices. (All apparently to avoid using DPDT Latching stomp-switches. SPST switches are much cheaper, even with the extra chips to latch their states.)
These days it has become cheap to put a $2 mini-brain at both ends of the wire. The pedal brain can scan many-many switches (more than can fit), trigger LEDs or even a text/graphic display, send hi-speed code up the wire to a similar mini-brain in the amp, which works its own dashboard light-show and the various switching schemes in the amplifier. The actual power needed may be low enough to run power down and data back on the same wire.
Fender Mustang II has a USB jack. You load software on your laptop (or I think iPhone?) and select several of 99+ different possible patches at one time. (You can do this on the amp but without a groovy interface.) A super-simple one-button no-LED pedal selects patch A B or C, clean solo bridge or whatever; then the iPhone can dump different choices for the next song. And it was not high-price: you could buy it as a basic amp and discover the wizz-bang later.