clock keeps resetting when turning on the headlights

[Jinster]

I have been experiencing a strange phenomenon.

If the ignition is on, and I go to turn on the headlights, the entire dash would switch off (indicator needles fall, clock resets, current mileage resets) for a brief second, and switch itself back on.

This only happens if the ignition is already on. It can't be re-produced if:
1. this has already happened once during this particular "ignition on" period - i.e switching the headlight off and on won't reset things again if it's already happened once during this one ignition on period

2. turning the headlight to on first, and then starting the car, avoids this problem

The battery is a good brand and only 6 months old. and the ignition switch was replaced last year.

Any thoughts?