I assume the dash air, radio, passenger air headlights, docking lights?, run off of the start batt. set. Is this correct?
All electronics that only run in the "key on" position connect through the start battery. Also.....usually the cig lighter plug.
We have two 12VDC outlets in the dash. The upper one is on the house battery. The lower one is on the chassis (starter) battery.
I don't remember how I determined it (I think from the wiring diagrams) but I have decided that my dash radio is connected to my house battery.
As Twig said, if the ignition key turns the radio off, it runs off of the starting batteries. If the ignition key has no effect, then it is connected to the house batteries.
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On mine, the radio runs off the starting batteries but the ignition key does not turn it off. If it is on the house batteries, the battery disconnect switch would turn it off. The only thing that will interrupt the power to mine is removing a fuse or disconnecting the house battery. This may or may not be the original configuration since the radio was replaced by the original owner to gain a color monitor for the back up camera.