You’ll struggle for such a thing as a wiring diagram for most boats like that. But it’s very very basic usually and easily traced out and determined.
As for the engine, what I'd do personally, is the following to start with
If she’s not been used for ages or of unknown health, take the plugs out her, feed a tablespoon of 2 stroke oil into each plug hole…let her sit for a while..and then see if you can turn the engine over by hand, using the flywheel. Go easy though, in case she’s reluctant with a sticking ring or two. Any real resistance at all…then morse oil and let her sit over night. Try again by hand. Work it a little at a time if need be. Be patient.
If she does turn over…make sure the plugs are ok and throw them back in for now.
I’d then crack open the gear oil drain screw for a look at the oil condition. Or if it’s present at all perhaps ! Nothing nasty in there…box that back up again.
I’d then make sure she has a clean power supply to her starter from the battery.
Then I’d say a wee prayer before cracking open the carb drain screws on the bottom of their bowls. Check the condition of the fuel line and primer bulb, belfry fitting to the engine and to an absolutely guaranteed source of new and fresh fuel and 2 stroke mix (at 50-1). Pump the primer bulb until fresh fuel comes out the drain screws mentioned earlier…box them back up thereafter. Say another prayer…then turn her over for a few seconds. All being well…choke on at the key…throttle open…crank her over again for a sign of life ! If she goes…then spend the money on plugs, gear oil…treat her to a carb clean too.
If all that fails…do a compression test on her to rule out anything nasty.