Diagnosis
A small amount of current is leaking through the trigger switch or control board, keeping the LED circuit partially active. This is a common electronic fault.
How to Fix It
Remove the battery pack. This is the only way to fully cut power and reset the tool's electronics. Leave it off for 60 seconds. Reattach the battery. The parasitic drain should be cleared and the light should now only come on with the trigger.
If That Didn't Work
The trigger/switch assembly is failing. Moisture or conductive debris inside the tool can cause this. The switch module is integrated with the motor controller and requires professional service or tool replacement.
Heads Up
A constantly lit LED, even dimly, will drain the battery pack over days of storage. Always physically remove the battery if you won't be using the tool for a week or more.