Since the GC can run off 12V, it must have a fuse for that right? If it doesn't, I'd go with the inverter. Mine has low-power warning and is fused. If they intended for the GC to be installed in a car, they know that the voltage will fluctuate. I'm positive that it will work by just connecting to any 12V wire just make sure you have it fused. The 12V sign is the universal for car use. They know that it's not going to be 12V solid.