The Z12 will draw about 8.5Wh of power with illuminators on and approx 3.5Wh with them off. So figure ~6Wh average over 24 hours. 6Wh x 24 = 144Wh/Day.
Using this site:
PVWatts you can determine how much sunlight would be expected to hit your panels for any given location. Its accurate too since it takes into account historical weather data. You need to plan for December usage since that is the month with the least amount of sunlight. For example if using for Birmingham AL for the location in that site calculator, a 100w panel would only produce 8kWh for the month of December or 266Wh a day averaged over the month. 266Wh (100w panel potential) - 144Wh (camera power draw) = 122Wh (excess). So yeah, a 100w panel would be enough to run the camera and dump excess power back power into the battery system which is what you want. Ideally though, you want to dump back into the system the same amount that you need to power the equipment in the same day. In other words, if your equipment is drawing 144Wh/day then you'd want to dump at least another 144Wh/day into the battery system that day. So a single 100w panel wouldn't meet this requirement using my quick calculations I described above. Keep in mind, those calculations are based in middle Alabama. The further north you go, the less sunlight available to hit the panels so the lower amount of power can be collected. If you are up in Minnesota for example, that 100w panel is only able to collect 6kWh for the month of December as compared to the 8kWh that the same panel will collect in middle Alabama.
As far as batteries, you can build your battery bank as large or small as you want but I'd spec out the battery bank to at least have enough juice (when fully charged) to run the system 3 full days with no sunlight at a minimum to cover yourself from lingering storm fronts, snow, rain, etc...
Your problem is you also need to run a radio 24x7 which will probably at least double the power draw depending on the radio. Probably looking at twin 100w panels at a minimum.
