electrical/electronic gurus

This could be a problem. The project, I mean. You really need a dedicated charger for the backup, and fully isolate the car system and the backup battery. This is because almost NO batteries, other than lead acid, are natively happy running off a car 14V system, which it really is. (Warm, running, the system is 13.8--14.2 nominal)

I no of no simple way to do this, other than to find a small lead acid battery, which you might be able to do. In that case you could use 1 diode in the main vehicle line. You would want the banded end of the diode towards the unit you want to back up and the opposite end coming from the vehicle power system.

Anode coming from vehicle system, cathode feeding to the backup unit. Backup battery connects on backup unit side of battery.

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