My 0058370 has the light "RPM Sensor loss", but when I move to manual start, it starts right up.  I was reading about stuff like the #18 wire, but cannot find a label on a wire that says #18.  

Is there a complete part that I should just replace?

Also I cannot find any pictures.   Anyone that can help would really be appreciated

The 18 wire goes to the coils and can be accessed at the flywheel housing to the right of the oil filter.  I am surprised it runs with this fault.
When in manual mode does the unit run for as long as you ask it?, while it's running you can page through the menu and see what the voltage and frequency output is. That might give us more info to help you.
I had this problem on my 7KW CorePower 5837. It turned out to be the contactor- fancy name basically for a relay. When the controller calls for the starter to start the engine, the contactor is what closes the battery-starter circuit. The contacts in these relays can corrode and fail. The controller knows it is calling for the starter to start but sees no movement via the rpm sensor. So it cuts out and records the error you are seeing. You may have been successul on manual mode, because the contactor fails intermittently until it fails completely. So you can get lucky in manual mode. Someplace to start anyway.
Geoff Z
This link will take you to Generac manual search. Enter your serial number and click get support. Every document/schematic for your generator will populate.