Are you sure it is not an oil warning light? My 15 Honda had a green light that stayed on all the time, my new Yamaha has an oil light but only comes if there is a problem.
i have a 1996 25 tiller the weight, i think is 105 poundsand my motor also has that light,someone said its the water or the oil, not sure if the water is to hot or motor hot.i would like to know 2