snipped-for-privacy@worldnet.att.net The most likely culprit is that the prongs of the nitelite just don't mate well with the contacts in the receptacle. Either get a new receptacle, a new nitelite, or put one of those "3-to-2 prong" thingies between the lite and receptacle to change the way the contacts mate.
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I agree. I was getting ready to suggest using a good extention cord for testing. Plug a nightlight into the extension cord and plug the cord into a known good outlet to be certain that the nightlight blades are making good contact with the extension cord. Then move the setup over to the questionable GFCI. The nightlight will probably work fine now, confirming the suspicion that the problem is caused by poor blade-to- recepticle contact.
Nightlights are cheap and somewhat poorly made devices. I've had some luck by bending the blades slightly so that they are farther apart. This increases the pressure between the outer surfaces of the blades and the mating surfaces of the outlet contacts.
Gideon