I am running power to some light off of the Battery post of the ignition and they work. They actually work regardless of whether or not the ignition is on or off, via a toggle switch.

I will try the wire from the Sol post to the starter, though that still leaves me the problem of the gauges, nav lights, and the power tilt not working (stern drive is currently up)

The black cable is part of what plug? What does a coil look like? should I connect it?