I am not sure what you are saying. Do you turn your engine off when you are still moving at low speeds? If so are you turning it off with the key or the kill switch? Why are you turning it off at all?
Or, is the light coming on when you are idling the engine? If so, is it the temperature light or the oil light which is coming on at idle? On my RIII it is the same light, but to the left of it is an indicator which shows which one the light is for. (A stupid design, IMHO.)
Or, is the light coming on and staying on after you have turned the engine off?
Which model RIII do you have? How many miles on it?