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, Hagstrom Ultra Swede
- Line 6 G30 wireless>Fulltone OCD>Boss DS-1>MXR Carbon Copy>Boss DD-5
- Fender Blues Junior or Vox Pathfinder 15R