The green oil lamp being on is a GOOD thing.....and.....a Honda thing. When it's lit it means that minimum oil pressure is present. You're supposed to worry when it's NOT lit when the engine is running. They do that with many of their models so it's not part of your problem I wouldn't think.
You may be correct about the trim sensor but I don't know. Maybe you could try unplugging it and see if that makes a difference.
I have no experience with the '98 50hp. nor have I ever dealt with a trim angle sensor. My experience with Hondas is primarily with the twin cylinder models.....20hp and below.
Hopefully someone else here will offer suggestions about that.
I am surprised though that you don't mention a red overheat indicator. And, I wonder, could some of that disconnected wiring be for that?
Sorry I can't offer much. I don't have a wiring diagram to consult to try and help you sort this out.
I ask about the overheat alarm because there have been several posts here, for several different models, that describe similar intermittent warning buzzer activation along with power loss (guardian mode) and in several instances it turns out to be debris build-up inside the cooling system.
Not saying that's what is happening with yours but just offering it for consideration.