Hi Eric. You are correct in assuming that there should be no connection between the battery negative and the engine block, except when the engine is being started or stopped.
If there is a connection between the Onan block and the 12v positive, I assume that you are getting the same voltage reading everywhere on the bonding system?
I would disconnect the battery cable from the solenoid and try again. If there is no voltage, then you can assume the connection is in the solenoid...I think. If you still read 12v with the battery cable disconnected from the solenoid, you have a different problem. On my Onan MDKAL 6.5KW, there is a ground (bonding system) connection from the inside of the electrical case on the aft end of the generator (that has the breakers and start/stop switches on the front). If I remember correctly, this connection should help prevent electrocution. If it is connected, which mine was when I purchased the boat, it could be the source of your voltage if anything else in the bonding system is inadvertently connected to the battery negative. If yours is connected, disconnect it and try again.
If anyone sees a flaw in my understanding or logic, please set me straight.