For a long while I’ve been looking for a cheap and easy solution for Raspberry Pi battery backup without lots of cost / complexity. This it it. That module is 12V to 5V at 3A, readily available off eBay. That diode is an old 6A4 but anything reasonably sized will do. A recommendation is a Schottky MBR1635 for low voltage drop. The connectors are Wago blocks. The positives and the negatives are of course common. The lead with the diode goes to a 13.8V PSU, the second lead goes to a 12V sealed lead acid battery, and the third lead goes to the input of the DC converter module, ie in parallel with the battery. The Pi hangs off the DC converter module’s output. It just works.

I am informed that a low value series resistor is sensible to limit current, should the mains go out for a significant period of time and the battery voltage drop too far.

Commercial product: West Mountain Radio Super PWRgate https://www.westmountainradio.com/product_info.php?products_id=pg40s

A lower current version based on mosfets https://www.novexcomm.com/FlintHillsRadioProducts.php

A build: power_gate_assembly_instructions_v2.pdf