DIAGNOSIS: Yeah, this one's common. There's a capacitor in the LED circuit that's holding a charge and bleeding it off very slowly. It's not harmful, just annoying.
FIX: It'll eventually turn off on its own, but to speed it up, you can 'force' the capacitor to discharge. After removing the battery, briefly touch the battery terminals on the tool together with a piece of metal (like a paperclip or the terminals of another, different battery). You'll see a tiny spark and the light will go out immediately.
IF THAT DIDN'T WORK: If the light is bright and doesn't fade, or comes back instantly with a battery, you might have a stuck MOSFET or other component in the switch assembly, which would require a board replacement.
HEADS UP: That tiny spark trick is safe for the tool. Don't do it with a charged battery attached, obviously. It's just clearing residual power.