Found a solution that met my specs:

APC CP12142LI Network UPS 12Vdc.

APC is a well-known reputable brand, this unit is specifically designed for 12v network devices (so it avoids the inefficiency of converting a DC battery voltage up to 120 VAC and then back down to 12 VDC) and it will keep my fiber terminal going for well over 24 hours. List price is $130; I got it for about $5 less (with free shipping).

I also bought a separate power supply for it (about $20) and an adapter cable to fit the terminal (about $7).

I had spotted this UPS a while ago, but it was out of stock all spring - supply chain issues I presume. I finally got it and installed it a few days ago. So far so good.