Having battery voltage on both sides of the solenoid at rest is not correct, right?
Kip, it is correct.
Electrically, the main posts on that solenoid are both connected to 12 volts (with the engine off). The input post is connected to the main Ford battery buss, so it sees the 12 volts of the Ford battery. The output post of the solenoid is connected to the 12 volts of the house batteries by a direct circuit through the circuit breaker (that assumes the breaker contacts are not totally open). If all is good, with the engine off, you will basically see 12 volts on every main terminal of the circuit---BUT it will be coming from two sources: the Ford engine battery on the input terminal of the solenoid, and the house batteries on the solenoid output and both breaker terminals.
IF everything is good, once you start the engine, the input terminal of the solenoid goes to 14+ volts (from the alternator feed), but--because the solenoid closed when you turned the key switch on--everything else goes to 14+ volts as well (both circuit breaker terminals and the connection at the house battery post); that's how the house batteries get charged.
So, if you have a bad breaker, how can you be seeing the 12 volts on the output side of the solenoid with the key off??
IF the circuit breaker is completely open--failed entirely--it would not conduct any voltage/current at all, so it would totally interrupt the connection to the house batteries and you would not have the 12 volts on the output of the solenoid with engine off. But when a set of contacts in a circuit go bad or get corroded over time, whether it be a circuit breaker, a switch, a solenoid, or anything else with mechanical contacts, they will frequently conduct the tiny amount of current needed to show voltage on a meter, but will not pass the heavier current in the circuit. That's why, when checking voltages in a circuit, it should always be under load to get an accurate reading. It is very likely that your breaker is conducting the tiny current load that your meter draws when you take a reading, but will not pass the much heavier charging current to your house battery circuit.
Mike