There is a neon bulb and, I believe, a resistor in series with it. Together, their resistance is enough to let the bulb glow for 80-500 volts (AC or DC) without hurting a person (at 120 volts anyway). At least that it what the one I use consists of.
What Adam says is usually true. However, if almost anything you try to run trips the GFCI, then they are not the problem and neither is the GFCI. Rather, some accidental contact is happening somewhere in the house wiring itself - contact between the neutral and ground further along on the circuit.
If earth were connected to the terminal where line (hot wire) was still connected, you are right. But hot/ground reverse (when it is literally true - which is very rare) would refer to when the hot wire has not been connected to that "line" terminal of the socket but to the earth terminal. So there is no tripping of the protective device. However, there would be a hazardous energizing (a making hot) of the metal frame of anything plugged into that socket. A shock waiting to happen.
That one (and most rocker switches) can take 12 gauge or 14 gauge solid (not stranded) copper wire under its screws, but only 14 gauge in the push-in holes.
Any tester can go bad. I recommend using a 7-watt or 15-watt bulb. They last for years. Also, I am not recommending this bulb-tester idea for confirming whether voltage is present, just for whether a voltage that IS present can operate a load.
I actually do favor pigtailing but not religiously... In regard to dissimilar metals, the metal spiral in a wirenut is also different from the copper it bites hold of. Your comment makes good points.
I see your point. I did show where to look for line and load on the GFCI. Another video of mine talks a little more about what load is. And if a person is not stuck on learning everything via video, my website tells a lot more about GFCIs.
It probably isn't designed to do that much switching, but might do OK. In addition, most kitchen GFCIs would turn off other outlets in the area, not just your light. Is that OK with you and your people?