Agreed, that is the proper way to check for a hard fault, however the problem could be a very small leakage only when 120V is present (and the very low voltage applied by the meter might not show the leakage). Or, as you mentioned, it could be intermittent and the meter might not catch it at that moment. Bottom line is it's a safety issue. Someone could actually be killed. If we have to explain how to use a meter, then that person should not be troubleshooting this problem! IMO...Put an ohm meter between ground and each prong (hot and neutral) with switch on and switch off. If you get continuity, then there is a problem. Nothing should go to ground, but that is why the GFCI is tripping. It will trip for even a momentary ground fault.