I've seen 12V automotive ones do that on truck and trailer tail lights. Because it takes almost no power to get an LED lit, I just assume it's a bad ground on another circuit backfeeding or moisture in a junction conducting across pins. I have LED strobes on my float that you can see dimly flashing at night in the winter when the roads are wet with deicer slop. Power bleeds from the tailight pin to the center pin on the 7 wire when it gets dowsed with salt water. Turn off the tail lights and the strobes go ALL the way off.

Kevin