I believe the radar will only auto power on for the 1st minute after it's auto powered down by the Edge. Once the Edge powers it down, the radar will blink a light (blue I think) for about a minute. During that time, powering the Edge back on will power the radar back on. After that time the radar needs to be manually powered on.
That matches my findings. The lights can can only be woken if they are in a state where the blue light is blinking. The radar only stays in that state for a couple of minutes after switch off, the headlight stays that way indefinitely. Just press the button on the radar and it will wake and connect thought, so not really a biggie.
I find myself having to carry around both sets of lights because the Varia lights let me down very quickly.