New to me Mercury 2.5hp 2-stroke outboard. No start? No spark?

[serpa4]

I have a new to me (don't know the year) 2.5hp Mercury. It was working fine two month ago. It sat on the back of my sail boat for two months till I needed it for my dingy. When I put it away, it ran fine. Now it won't start. I have replaced the fuel and replaced the plug, but it won't start. I tested the cutoff switch and it has continuity. It doesn't even catch like it is about to start. I held the spark plug against the engine bolt to see if there was a spark jumping the plug, but I didn't see anything.
Any suggestions on what to check? Can the coil or CD (I think it is a CD) be tested?

 

[serpa4]

Engine pictures

 

[Scott Danforth]

when you tested the cut-off switch, was the continuity there all the time, or only when you pressed it?

if there all the time, you have a bad switch, should only be there when you want to stop the motor.

 

[racerone]

Perhaps pull the flywheel and see if there are breaker points that need cleaning.