[BusNit]

In my quest to identify what goes where and how for my upcoming Lithium house battery project, I found this doohickey. Looks like it would be powered on with another switch to cut off power to the inverter but I can't find said switch. Am I correct to think this is some sort of electric cut off switch? Top wire goes to inverter bottom tied wires go to separate battery banks for inverter. Ultimately, I need to figure out how to isolate house from engine since each will have its own battery chemistry. Also when I shut off Aux battery switch in electric panel of engine compartment, I still get power to inverter and said solenoid. Thought those would shut off but they don't. My digital voltmeter at dash does lose power.

[Richard]

Thank you @kaptain, I did not know that was a resettable breaker. Thank you for the correction, and keeping incorrect information off the forum.

[kaptain]

In your photo, there appear two circuit breakers. They are considered self-reset-type circuit breakers or thermo breakers.
I don't know which one you are asking. But the large (black color, hexagons/rectangular shape) one, with two (2) thick red wires, is obviously for large amperage.
And the small rectangular shape one with 2 small/thin wires connected activates is the same thing, but obviously activates on smaller amperage.

How do they self-reset? It works on the principle of temperature expansion with metal (conducting amperage). When large amperage passes thru the metal contact, heat is generated, so contact metal expands, thereby cutting off the circuit. Once it cools down, it restores contacts, allowing current to pass through.

How do you test them? Remove and disconnect the wiring, then use a multimeter to measure between the two (2) contacts. They should normally be closed, reading should be nearly 0 ohms. If it's open, then the circuit breaker is bad.

[BusNit]

So is it just a terminal block to connect the three large wires? Two on the bottom (Batteries) and one on the top goes to inverter. I know the smaller is a self resetting breaker but no idea what it serves. At first I thought the large insulator block was some kind of solenoid to disconnect the inverter power. So much to take in, I may just say screw it and put lead acid batteries. I still don't know how to isolate the generator's 12v output when it too is running.

[kaptain]

So is it just a terminal block to connect the three large wires? Two on the bottom (Batteries) and one on the top goes to inverter. I know the smaller is a self resetting breaker but no idea what it serves. At first I thought the large insulator block was some kind of solenoid to disconnect the inverter power. So much to take in, I may just say screw it and put lead acid batteries. 

The large block is also a circuit breaker, although the bottom terminal is connected to 2 wires, one thick and one thin wire. 
You can consider them as simple terminal blocks for connecting wires, but that's only true when everything works normally.
Once the current flow (or temperature) exceeds its rating, it will disconnect.

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I still don't know how to isolate the generator's 12v output when it too is running.

I think your generator output is 120/240V only and doubt it has 12V output. Your inverter charger is always ON (unless you manually turn off the disconnect switch) regardless its on shore power or on the generator. When you have both shore power and generator power, its the work of your transfer switch that selects which power to use.