Next Project - Inverter and Dual Battery Setup...few questions.

[PARAGON]

You don't want all of that, I don't think. The DC outlets are powered all of the time. So the add-on thingy would be draining down along with the stock battery assuming that it's a simple circuit that charges the thingy's battery which many of these thingies are.

A better solution would be to buy a solar panel and have it wire to trickle charge the battery. You could also wire in a plug that would allow you to plug in a trickle charger and charge it from your home's outlet.