Full function = higher charge settings. If you have a higher amperage charger, you're golden.
Yes, the Battery Minder Jr. is a good maintainer, AFAIK. It is certainly miles above using nothing.
FWIW, I've over-wintered many batteries and left them with no charger on (but fully charged) or used a maintainer. I've had better luck with a trickle charger on them 24/7. Some of this might be environment or location of storage.
Now, my trailer is stored outside with two banks being charged by the solar module. They seemed to have come through the Winter in fine shape. That's a good thing as I don't like lugging around batteries so much, anymore.
