Indeed! I third that. I’m not surprised George sees a good Vrms correlation between the input and output voltages on these things. As far as I can tell, there’s no real regulation. The amplitude of the mains/primary swing seems to directly impact the amplitude of the secondary/output swing. For kicks I plugged an Osram ET-Redback into a variac and put a 20W bulb on its output. The variac knob appeared to be a very effective (if impractical) dimmer.
I then hooked the output of the ET to my scope (still driving the 20W incandescent bulb). You can see those big yellow blobs occurring every half line cycle (10 msecs) and when you zoom in on them, you can see a square wave at about 75kHz.
George, at best you might be able to deduce Vrms of the line voltage from the output, but as Robert and Greebo have pointed out, if you want to measure real power, you need the voltage signal to be an accurate scaled down version of the AC mains voltage signal, and it’s clearly a million miles from that.
If you’re only interested in measuring apparent power, then the mains voltage you deduce from the ET output might be more accurate than just a hardcoded 240V.