Battery Disconnect switch.

The disconnect solenoids are usually (always?) the latching type so that no voltage/power is required except when switching. There are two signal terminals and reversing the polarity (swapping plus and minus) switches the solenoid from one state to the other. The solenoid may need to be replaced. I would put a voltmeter on the two terminals and watch while someone presses and holds the switch one way and then the other. If the voltage is there and reverses polarity but the solenoid does not activate then you probably need to replace it.

That switch controls Big Relays, picture in link. This is just a picture so you can look for it. https://www.youtube.com/watch?v=UGxJs5XaSWY

Check near the battery or fuse panels. Mine are located in the front. Others in different places. Wrap them with a mallet and try the switch inside again. Works best with two people, one pushes the inside switch and the other one listens to see which one is controlled by that switch.

What is the voltage on house batteries?
The switch operates a relay, that with low voltage will not engage.
At least that is standard set up. Can you access the relay and take picture?