Spotlight doesn’t work on a GFI protected outlet

I'm dumbfounded. I have an outdoor GFI-protected outlet that needs to provide power to a photocell controlled spotlight intended to illuminate an American flag at night. I've tested the spotlight from another outlet by plugging it in and covering the photocell simulating darkness and the spotlight turns on as it should. When I plug it into the outside outlet it does not turn on when I cover the photocell. I've tested the GFI by plugging a lamp (two prong ungrounded) into it and the bulb lights indicating there is power on the plug. When I push the TEST button on the GFI, it trips and the lamp goes out. Pushing the RESET button restores the GFI to normal and the lamp comes back on Yet the spotlight that has a three-prong grounded plug will not light. Any idea what's going on as it boggles my mind.        Dan