Don't know about today's stuff, but in bygone years every mechanic had a remote starter button in his toobox. Simply clips to the starter solenoid. Should have them at your local auto parts store.
Actually, it looks pretty good. You can squirt a bit of oil on the seal and rotate the shaft a few times. See bubbles? If so, the seal is leaking. People tend to over lube the mounting rings. Just a light smear is all that is needed. Excess gets lignified by vibration and fouls the breaker...
As said, generator wires come in from side plug, and won't be connected to anything if no generator kit is installed. They are yellow and blue wires. But people often would appropriate for some other use.
Can't make out exactly what wires you are holding. Probably generator wires for use when a generator kit is installed. If no generator, the wires won't be connected to anything. Unless somebody has connected them for some untended use.
How's the pinion bearing? It's cast in place also. Since you have a mill, you probably can bore out the old bushings and make new ones. I assume you have the skills?
I'd use 932 bearing br0nze if I were doing it.
That sludge in the can is the oil you put in the gas. Normal. Don't jump to...
Not the rectifier. I think you probably have a wiring problem. Loose or shorting wires or such. Check the 12V supply to the tach and/or the ground. Possibly even an intermittent ACC feed from the key switch.
Ther is a groove around the splined area of the drive shaft, for an o-ring. The splines are to be lubed with a light coat of grease upon assembly, and the o-ring keeps water out of them.. If water does get into them, the splines will rust away from the steel crankshaft. The drive shaft...