Pretty sure the light in mine used to come on when the lights where turned on to either side lights or above.

For those who's light isn't working at all on most there is a renewable bulb, some earlier ones are soldered in, to access it you need to remove the clock from the roof, two screws and disconnect the round multiplug, then the back of the clock unclips to reveal the bulb.

The sidelights dimming when ignition on... that's called dim dip light which essentially powers the dipped beam system at half the power of the standard dipped beam when set to the side light position, it stops you driving the car on a pair of 501's by accident.