Electronics novice here, but it could be one of the leads on the LED has gone askew/awry. If you can, take the unit apart and look for any obvious signs of damage or weirdness. Take a pic or and post it if you can - that'll help the more experienced peeps on this board diagnose the problem.
If the pedal still works fine (sounds like it does?) then I wouldn't sweat the LED for now.
- Fender Standard Telecaster, Fender Classic Vibe Strat
- Dr. Z Maz 18 Jr. with Dr. Z 2x12 cabinet