Start first with the feasibility. When you say, "always on with low power draw" what, exactly, does that mean? 1 watt? .5 watts?
It's probably easier to translate that from a requirement like: Must function continuously for 2 weeks on standard 12 volts, X amps battery without consuming more than X% of the battery's capacity.
Then you can do a quick back of the envelope just to see if it's feasible.