The marked photo shows what I found and measured. My sense is that there is something amiss between the house battery and the power relay under the hood: 12V chassis power is picked off the bottom side of the relay and sent somewhere else, presumably to be selectively sent back to the coil in order to connect the + sides of the chassis and house batteries.
The two solenoid coil terminals are electrically connected to either side of the coil - one side to chassis ground. When 12V is put on the "high side of the coil it will energize the relay and connect the two large terminals, thus electrically connecting the batteries. But there is no 12V coming from the house end of things to connect to the + side of the chassis battery.
None of this answers the question about the working order of the house battery relay and solenoid. All I know is that the fuses associated with that component are OK; beyond that I don't know. That will be step #2 for another day.