I'm no expert (though I play one at my day job), but my guess is the fuel pump. I hear somthing like what you describe, and I do not have motorized headlights (Litronics).
I have a 2001S and i hear the same bzzz with an electronic ticking at the end which comes from the left of the car. I pulled out the carpet cover and i have noticed that it comes from a black switch maker Bosch ( or relay, i dont know exactly what it is but according to the book i've seen that subject is attached to the hydraulic unit anti lock brake system control ). Perhaps an expert from this forum can help us and clear out this question.
DING DING DING!!! We have a winner. It's the fuel pump. It pressurizes the system prior to starting the car so it starts faster and easier. Eventually when the car is off the pressure will bleed away through the regulator back to the tank (in the front) so it re-pressurizes when you turn on the key. Most cars do this (very few dont).
It should only last a few seconds, not like a minute or anything tho...