This issue is now fixed ! The intermittent headlights were caused by the electrical relay that lives between the control module and the headlights. It was faulty - hence the problem.
It is a rare problem but cars don't have a simple circuit to the headlights anymore and these things happen. The dealership swapped the relay from the fog-beams to the headlights which fixed them until they could replace it with the correct (relay) part. The faulty relay was wounded but not dead - which caused the confusion.
It is rare enough problem that the mechanics at the dealership didn't believe there was a problem until my car was ready to replicate it for them on my fourth visit there. And letting all know my patchy understanding will help the 0.01 per cent of drivers of modern cars that this will happen to (my guess).
That's it. (I originally posted this solution late last year but this webforum computer server crashed and lost it).
good luck and CheersGo to the full post