Alright so you listened so i'm back. I had your exact problem. If i tell you i spent a solid week checking every wire, every connection, every ground. Mine is a 86'. So what i did in essence is create a new harness.
I ran the jumper with a toggle to the helm and marked it ign. When i want to start the boat pump the throttle, and flip the switch. And i crank the starter with the key. The boat starts, i run it to where i want, when i want to cut the motor i turn the key to off it will still run cause i have power to the coil. Then i flip the switch off.
I wired it like a old style race car and they still do it that way. Way old boats, model t's, and a bunch of industrial equip. are wired that way. Aircraft are wired that way also.
What i think is you have a dirty connection at the starter, main ground may be bad, or the slav solenoid if you have one or relay, could be bad or not grounded or the connection there bad.
Some solenoids have to be grounded by the base, remove and clean the base and the mounting point.
If you chose to start cleaning connections,use 100 sand paper. Make sure you disconnect the battery.
Now look at the starter see a square box on it, could the connection be bad to it.
You main plug should be held together with a wire clip, take it apart, it green and corroded ?
Now understand what i do, i do cause i have 45 years of knowledge. I want to live a long life, so i make sure everything i do i do safe.
About those 2 wires hanging, You have a trim indicator ?
With the jumper you say it runs and doesn't cut out ? If yes then it ain't your coil.
It cranks good when you turn the key ? If yes then you might chase this and never find the problem. Consider this one wire going in to the main plug bad in the plug itself. One side or the other.
My main barrel plug is history when i made my " Harness " When i pulled my motor i never undid it anyway, i disconnected everything from the motor, and marked them.
Ok to finish a bad tach wire will kill you also. People don't really understand that also.
You had it running water going to the drive ? What did the gauges do ?
Also i have no man overboard lanyard switch.