That's what confused me about what electricity "is" and reason I posted back on page 17. Without an understanding of both the microscopic behavior of 'lectricity, and how that relates to Maxwell's EM, I could be a bit lost. I don't think I am, but experience fills in the gaps, rather than ever having a good understanding at a theoretical level. In other words, I am a bit lost, even though in practice I'm not. I don't "believe" in surface charges, not because I don't think they happen, but because I don't know what it really looks like. Dumbed down diagrams in high school, highfalutin maths at university isn't evidence of fact needed to form what I would loosely call a belief. Anyway, rant off again, but I think this is pretty much universal for engineers, even RF engineers.
This new point is like Mehdi and Walter Lewin's 'disagreement' about voltages in a loop including resistors in a changing magnetic field (I heard of during this thread, haven't watched it all) - in this case current induced in a sense resistor (standing in for the lamp) without dropping voltage (or perhaps vice versa). If such things didn't happen, there'd be no point having more than 0 turns in a transformer, yet there is room in very well-accepted "theory" for arguments to develop, like the Poynting thing not first covered by Derek, but he successfully lit the fuse. I'm kind of in awe at how difficult this simple question has become!
To my mind, making that sense resistor smaller than about 1% of the 1m in question will mean its antenna effects won't have a significant affect on timing, smaller will help a lot with parasitics for measuring timing to even 10% of 1m/c.
If not going the VNA+IFFT or fibre optic transceiver routes, I'd make a moderately high voltage fast step generator, to ease the building of a 1k (or 2k, for 7.2W 120V bulb) load into 50 ohm coax needed for any fast scope or RF gear. Battery powered, self-triggered or a button (string to pull on), with some nod to the way the battery exists in the video's experiment, so that means a fast-closing switch (small GaN fet) even a mercury wetted relay. It doesn't need to be perfectly isolated or balanced, but obviously can't have wires dangling off it or an enormous shielded box.
Sense end I'd probably try a few turns around that amorphous core before giving up and making a simple differential system of centre-tapped 10:1 dividers, ie 500 ohm to 50 ohm with ground in the middle and 2 scope channels, and if that didn't cut the mustard with viewers, then differential amplifier(s) good for a few GHz. Or something equally unpleasant to 'lash up' or buy for one test. Good scopes probably come with 500 ohm probes (there we go; Tektronix P6056). Duplicated for the send end, trigger off either. All checked for behaviour in and out of circuit.
And that's pretty much it - press the button and watch what happens. Only problem is if using a switch (rather than voltage source), the rig will be a very effective antenna, solve with averaging and high trigger level.