Okay, couple of things.
Since it does NOT "clunk" when you pull the power lead off the coil, that is significant.
Seriously.
Now, a really stupid question.
Do you have a radio in the car?
Or, maybe a NICE radio and an amp?
Like, power supply "popping" the speakers?
Is the radio/amp on, and just turned down?
Next, this does not do it when you are head-under-the-bonnet.
But, it does when you are in the driver's seat.
Like, maybe, loading something with the big round end on the suspension you are not loading when you are outside the car?