This happened on my Gen 1 Mille and my mates Gen 1 Tuon, as it looks the same setup on the RSV4. Check the brake micro switch cable which is attached to the rear brake pedal. It's a black cable with a galvanised nut end. Shit gets past the actuator pin seals and the rear light stays on.
If you look at the 3rd picture here, you will see it to the left of the engine casing going down to the brake pedal and in the next picture it is left dangling over the swing arm.