The light is an immobilisor security light that should flash every couple of seconds when the immobiliser is active. (soon as the ignition is off and key out). but goes off completely after a couple of days to protect the batt.
An immobiliser light constantly on but an otherwise running fine bike may point to the immobiliser ecu being dodgy. The only other time i can think of when the light should be constant is if the immobiliser refuses the key code but then it wouldn't start unless bypassed.