I think the easiest way to get standby power is to buy a UPS unit
and modify it. Remove the battery(s) and put a connector on the 
back for external battery. Some are 12 volt and the larger ones
need 24 volts. You might need to add additional cooling fans 
inside where the  batteries were for continuous operation. Some 
of the UPS units I have used got pretty hot by the time the batteries
ran out and they were evidently designed so that they ran out of power 
just before they melted down. A UPS would take care of the switchover
when the power goes off. 

I have a 250 watt UPS that I put Binding Posts on the back so I can
add more battery capacity when needed. It uses 12 volts.

I also have a 650 watt UPS that uses 24 volts.The smaller one is sine 
wave and has an internal fan and thermal protection. The larger one
has NO fan and would need one for continuous operation. It does 
have a thermal cutout which would shut it down when it gets too hot.

Both of them have light bar meters to monitor the battery voltage.

Large RV batteries rated for deep cycle
are reasonably priced and can be found at places like Walmart

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