Continuous operation of a general purpose relay?

Hello, I have a circuit that will need to return connected hardware to a default state if power is lost. The hardware can handle continuous voltage, so I’m thinking a simple solution would be to use a battery to provide that fallback power source. To avoid draining the battery, I’d like to connect it through a relay on the normally open contact and energize the relay directly from the main power supply on my board.

Do I need to look for anything in particular to make sure the coil on the relay I choose can sustain constant voltage for potentially months at a time without damage? Or, is there another similarly low cost and simple solution you’d recommend?

The circuit runs on 12VDC from a [Mean Well IRM-10-12 (specification), and the relays I have on hand are OMRON G5LE-14-CF 12VDC (specification). I don’t see anything on the relay documentation that specifies a maximum duty cycle.