The message indicator light will not stop flashing

The term we used for this back when I worked for the phone company was a "stuck message waiting indicator" and the way to fix it was:

Call yourself and leave a message.
Hang up and wait 2 minutes (we used to say 5 minutes, but 2 is plenty)
Retreive/delete your voice mail message
Hang up and wait 2 minutes


That should clear the blinking light.