The OZO Power Cable has a 2.5V dropout voltage. That means a power source that supplies approximately 14.5V or higher is needed to maintain 12V. Lower voltages produce about 2.5V less than what is incoming until you reach the low-voltage dropout protection cutoff of the regulator.
Most 14.4V camcorder batteries supply voltage above 16V when fully charged, and the OZO Power cable can work with 24V sources as well (or any source up to 40V). If you find that your batteries don't maintain voltages above 14.5V long enough for your purposes, you do still have options.
If using a block battery, utilize the 28V source. If using 14.4V camcorder batteries, there are two options; both of which involve using two batteries at once. The best option being to use two battery plates wired in series to produce around 32V when the batteries are fully charged and about 20V when fully depleted. The second option is to use a widely available "shark fin" mount that pulls power from two batteries at once without changing the voltage (something similar to: http://www.antonbauer.com/en-US/Shop/products/batteries-and-power-accessories-qr-hotswap-gm-adapter-8075-0023). Using this adapter, the batteries will drain more slowly, and you will have a longer run time above 14.5V.