Re: 1987 evinrude
The 9.9 and 15 hp motors do not have a solenoid, but use a heavy duty push-button switch to supply the current. They do have a neutral start switch between the switch and the starter, which is a safety measure to prevent starting the motor in forward or reverse.
For a ton of information on these motors, look up "LeeRoy's Ramblings"- he posts here as "the machinist". In one of his articles on these motors he gives the number of a similar heavy duty switch available from Radio Shack that's cheaper. I took a quick look but couldn't find it easily (these are long articles, full of information).