Honestly,
I don't even know how these touch lamps work.
Neither do I, but I do know that they have an r-f component connected
to them, because when I play an am radio and turn one of them on in
the vicinity, the static drowns out the radio signal, and when I turn
the lamp off the static stops. It would appear to be an electronic
switch that is activated by the change in the capacitance to ground
at some point that occurs when you touch the metal part of the lamp.
But i don't know anywhere near enough electronics to explain how
something like that might work.
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