Here is some LCM (Lighting Control Module) information:
http://www.cvpi.org/archives/p71interceptor/lcm/wsdindex.html
Electrical Ghost and fun with Fords - sounds to me like ya might have something grounding etc.?
Does the car do this when it is not in motion = vibrations?
If only when in motion,,, then my bet would be on a ground or wire split somewhere that is grounding out or arching while the car is rolling and vibrating thus causing a wire somewhere to do something it should not be doing contact wise?
If the car seems fine just idling (with all systems turned off) then perhaps it may be a system related issue?
If the same thing happens on idle then (I would) go through and see if any systems can trigger these symptoms in your car one by one isolating each system e.g. AC, climate control fan, interior lights, exterior lights, put it in gear and out of gear, hit the brakes, turn signals, windshield wipers etc. etc. etc. (I would also run them for more than just a turn on and off or a few minutes) on all electrical systems you can control and see if you can isolate it to a system area?
Really just a process of elimination IMO running down electrical ghosts from my (very limited experience)..
I did have several electrical bugs when I got my most recent P71 but all normal e.g. Wig Wag wire clips, old LCM relay, horn etc. so,,, I got lucky..
One last thing (don't know how long you have had the car) is perhaps look at your CPU Unit and see if you can spot any areas where someone might have been doing some probing around checking wires?
This always scares me, had mine had any indication of this then I would have walked away from it, Ford electrical systems are known for being hard to run down sometimes IMO
If it was me and none of the above worked then I would break out my shop manual and meter and just start going down the list of relays checking resistance etc. etc. down the entire list, same thing a dealership or shop might do...
Another good one (perhaps first since the car still is rolling) is to perhaps try an Auto Zone, Advanced Auto etc. and see if they will pop it on their diagnostic tools and if they can spot anything odd? They will often do this for free but are tending to do it much less now due to my bet some law suit or insurance thing, any shop or dealership is of course going to charge you for this but of course it is always an option..
Best of luck!!