That's a kinky get up you've got right there!
From what I've "worked out" with my limited electrical knowledge, with a 12v you can get 2-3 hours, providing you have a battery rated with high enough "amp hours". It's all very confusing, but it looks like a 12v leisure battery (as suggested above by tony.r123) would take 10hrs sunlight to charge from a 5W solar panel and would have far higher "amp hours" than a car one. Just need to work out what draw some lights would take and if I'd need an inverter....