I installed a 3mm blue LED (Vf~2v according to Tayda) with a 10k resistor (1/8 watt) and everything worked on a 9v supply.
The LED went out VERY shortly after I switched to my 18v tap and the compressor stopped working. I crossed my fingers that the dying LED just gave those 18v a quicker path to ground and, sure enough, when I de-soldered it and ran the pedal at 18v without an LED, everything worked (to be honest, I was pleasantly surprised by how much BETTER it worked at 18v!).
Looking back, I think the 10k was enough resistance but the calculations show that P would work out to approximately 0.16 watts so that was at least 0.035 too much for the 1/8 watt resistor. I replaced what I had with a 1/4 watt resistor at 15k and that seems to work quite nicely!