As stated above, shutting off the circuit breaker to your battery charger / converter will stop it from consuming 120 volt power to keep the battery full overnight. However that same circuit breaker might be supplying all the 120 volt circuits for say the bathroom, basement storage compartments, and such.
You could unplug the converter/charger. If it is easy to get to, this might work out well. On my RV, I have a 400 watt solar system and my converter/charger is actually a inverter/charger and it is easy to shut it off when not needed - most of the year.
What about the solar system? A pair of 140 watt solar panels will supply your 'normal' needs. You can buy those here for about $229 each.
SunElec.comAs for mounts, buy a few feet of 2" angle aluminum (Home Depot) and cut to 6" long. Drill three holes 3/16" for #10 screws into the roof, and 5/16" for the bolt into the solar panel frame.
Wire: #10 romex from Home Depot, grey water resistant UV resistant and direct burial type. Run the wire down the back of the refrigerator vent to the basement, to the batteries.
Controller: Get a PWM 20 amp controller they are cheap now, about $20. It will turn on the solar when the battery is low, and shut it off around 14.0 volts.
Wiring is pretty simple. Just keep the ground wires to one side and +12 on another.
Good luck,
Fred.