Hi,
i took a 5mm hollow plug soldered it to a good wire, some cable shoes on the other side for connecting the battery. The Mini needs about 1 Ampere. So you might think it works 280 hours. But i recharge it every 6-8 days. A smaller battery does it too but you will have to recharge 2-3 every days. I had a 60Ah battery before the big one. Try it, but pay attention to the polarity. The Zen Mini is very robust with the voltage from 10 to 12.8 or more. It switches off if the battery gets empty and you can charge the battery during it is connected