Have you seen this video? https://youtu.be/2Vrhk5OjBP8

I liked the part at 17:30, where he explains how the capacitive coupling between the wires produces current. Interesting. Did you mean this video contradict something in my answer? I don't see, on the contrary.

coquelicot‭ The whole problem was formulated in an ideal manner, so the lamp would glow instantaneously. It no longer matters that the "bulk" of the current would only appear after 1 s due to the transmission line effect. And it will not start glowing with a brief pulse, then wait for the rest, because the induced current is constant; you can see that a few more seconds after that, at 18:05, there's a small plateau which is sustained. When the ends are opened, sure, it drops (there's an antenna, it can't hold DC), but the problem in the OP has shorted ends.

@a concerned citizen. Thanks for the feedback, really interesting again. I suspect your alleged SUSTAINED plateau is an artifact of the experiment. Of course, everything is continuous in classical physics, but the meaning of what I said is that there should be a small peak, then the current should decrease, and then increases again toward the sustained regime. I need more time to analyze the video and to find the flow in the experiment. Otherwise, everything seems to me completely illogical. How could a closing switch maintain a continuous plateau by capacitive coupling in the wires when the AC part of the current last only few microseconds? Eventually, if I am unable to find the flow, I may update my answer accordingly. In the mean time, do you have some insight about how this can happen?

coquelicot‭ Well, if it was an artefact then it's on the owner of the video, feel free to ask him about that. I happen agree with the outcome, but that's just me.

@a concern citizen. I meant, do you have some insight about how this apparent paradox could happen, not the alleged artifact.

@a concern citizen. No need, I think I have the artifact: the line in the experiment has obviously a non negligible inductance. So, when the switch closes, the inductance of the line creates a relatively slow linearly increasing current, which can induce, indeed, a plateau by capacitive coupling in the other side of the line. In the mean time, the signal has come back and the sustained regime begins. Hence the observed phenomenon. In the ideal experiment (or with a coaxial line), the inductance is null (or canceled by the capacitance of the line), and this would not be observed. I will update my answer according to these insights, and explain everything, but a bit later this week, as I am busy. Thanks again for all!