I always thought the chief advantage of HID electronic ballast was for the flicker reduction.

Yes, I believe it is too, yet many companies will advertise massive savings when switching from magnetic to electronic. I remember seeing one 400w electronic MH ballast advertise a 20% energy savings (so 370w? Assuming a conventional magnetic uses 450w) and a light output increase of 10-15% ...thats impossible.

The advantage of electronic is, it offers, rather painlessly, dimming of the lamps.
If that is used to compensate the efficacy variation over the lamp life. it may save about 15..20% of the average energy use with most MH's: New lamp has reduced power so it's output matches the EOL lamp at full power and the ballast power is gradually increased over time so, the lamp output remains constant. In this way most of the life the lamp consume less than the rated power, while the output still matches the requirements. But such systems are quite rare and are sensitive to maintenance errors (ballast needs reset when the lamp is replaced - when not done, the system does not save the energy), that is probably the reasons, why it haven't become so popular...

I'll try the trick with a shiny metal object one note and let you know its too cold and wet at the moment tho. Also I mite try walking past with an AM radio see of I can pick up any noises if I do that will probably mean electronic HF ballasts. Or I could just fone the power company and ask although they mite get a little annoyed about me asking I'll be brave and try

If you drive by in a car, you may notice the flicker when looking at the buildings when the car is in motion (be safe, do this only if you're the passenger). If you're in Europe, this will be more noticeable as the flicker is slower due to the 50Hz.

Another way of finding out if you can't be close to the light to wave an object would be to use a digital camera, preferably one where you can set the shutter speed. Using a relatively slow shutter speed, such as 1/30 or lower, take a picture of the lantern in question, but move the camera very fast as you press the release (start moving the camera before pressing the shutter release). Looking at the picture, you will see a line that follows the camera movement. If the line is dotted, you have a magnetic ballast.

most cameras pick up the 60hz cycle too, the light will appear to be flashing or you'll notice dark bands moving horizontally across the screen when aimed at the light. Youll only get this with line frequency fluorescent and HID ballasts, incandescents, halogen and HF driven lamps will not exhibit this on your camera. Some high end, expensive cameras have a feature that automatically detects magnetic fluorescent and HID and changes the frame rate to reduce that.