If the GFI only trips when the head is connected to the power supply, then I'd concentrate on closely inspecting all the cables, connections, and what's in the head. All it takes is damaged insulation, dense cobweb that got wet, dead bug across terminals, etc to cause 5mA or less of leakage. A dead short will trip regular circuit breaker. Tripping GFI is already indicating there IS a leakage somewhere. If you do connect it to non GFI outlet, please be careful. You already know there IS a problem....

Michael has a great idea. Yup, open return (white wire) will cause this condition too....