Anbaric heaters: 1 Kim: 1
Seriously, there should be some sort of standard for the blinkenlights on these things. We've got two fan heaters, each with a thermostat, heater power selector and neon lamp. On one of them, the neon lights up to indicate the presence of mains power. On the other, it lights up to indicate that it's currently blowing/heating. I've also used an oil-filled radiator recently with the same control arrangement where the neon means "thermostat below set temperature" regardless of the power setting.
Anyway, for the avoidance of doubt, exactly none of these are the correct, useful behaviour. What you want a blinkenlight to do, first and foremost, is tell you whether you've left the heater on (and if it's currently stopped by the thermostat on account of the room being warm, it still counts as on) so you can leave the room with a reasonable assumption that it won't start up and set fire to things or waste electricity.
To that end, I've just re-wired the first one so the light comes on whenever the power level isn't set to 'off'.
I failed at gaining access to the second, for while I was equipped for stupid triangular security screws, I wasn't equipped for them being deeply recessed in a hole too narrow for my bit driver[1]. Bastards.
[1] This is known as "The SE-30 Problem", for reasons that will be readily apparent to anyone familiar with the works of the Not-Yet-Mega-Global Fruit Corporation of Cupertino, USAnia.