A fully charged deep cycle battery should allow the pump to run much longer than 12 hrs. The pumps only draws about 1-2 amps on my setup, maybe yours is different with more taps? Have used a 70 watt solar panel but I don't have good sunlight where my pumps are, and they do not provide enough charging. But my NAPA 8270 deep cycle marine battery will last about 30-35 hrs with my 4008 Shurflo which is about the same power as yours, maybe a little higher. Suggest at least a 100 watt solar panel with charger. Still might not carry you thought those all night runs followed by a cloudy day, you might have to charge it a couple times during the season, depending on the weather.

Dave