Harry Bloomfield wrote:
Roger Mills submitted this idea :
Clearly, I must be missing something! Anybody know what?

When the switch is off, there is potential/ voltage across the two
terminals. That potential charges either a tiny battery, or a
specialised capacitor so it has a power source when the light is on and
there is no potential across the switch.

Most likely problem if the fuse has been blown by the lamp, is that the
Triac has also been blown or possibly the relay, if it uses a relay for
switching.
Even when the lamp appears to be on the capacitor can be charged during
the first few degrees of each cycle without any noticeable effect on the
lamp brightness.