To isolate, when it's on a no start situation, unplug the main harness and jump it at the motor (solenoid). If it runs then you know it's not at the motor but in the box or harness.
You will have to plug it back in to turn it off.
How big of a barrel are you using and how long have you been running it this way?
If it's been awhile since it's been under a load going full bore it will oil up pretty good.
Is this an electric start....? Tiller motor?
Anyhow, could be many things. Weird partial problem with the kill switch, or neutral locator switch on the starboard side....shorting wire.
This assumes the engine itself is mechanically fine.
The shift switch that they originally talked about is a switch that kills half the outboard momentarily when you put it in gear making it easier on the gearcase.
Not sure where it's located or if you have one.
When Chris said near the shift cable he ment back at the motor.
I didn't think it was a g2....are you sure?
I have the g1 115 and it has the 6 cylinder foot.
My brother has a g1 ho and the only thing I saw was water pickup is different and a few other things.
I was also told in the g2 you could get the 3 cylinder and the 6....6 had more torque.