i have a 1998 or 1999 20 hp 3 cyl. Evinrude that has a red light on the front of the motor next to the pull rope that comes on when I start the engine. It didn't do this the last time I took it out fishing. But when I hooked up the water hose to the "ear muffs" to run it in my yard after sitting up a few months, I noticed the light on when I started it up. I have no owner's manual as I bought it second hand. There is no warning buzzer accompanying the red light. It has oil injection. Could it be an oil injection warning? or is it a heat warning sensor that is getting a false reading? And yes, the water pump is working as I can see water coming out of the "pee" hole. 
