i would plump for the left hand side multi connector under that fairing infill only 3 screws to remove it and the multi connector is right in front of you.
Turn ignition on, put light switch into the headlight on position and give the multi connector a good wiggle if you lights flash on and off you have found the problem, but if they don't you should still not rule that out it maybe that the wire has completely corrode through causing a complete break.
Good luck
So many Fazers seem to suffer with this problem, water from either riding in the rain parking the bike in the rain especially on the side stand or too much washing, the later being my problem.
I had exactly that, headlights would go out intermittently and then come on again, sometime refusing to come on at all ride over a bump and they would come on again.
Corrosion in the multi connector, some of the pins and sockets in there almost gone, I cut the offending wire either side of the connector and linked them together by soldering them and heat shrinking them. sprayed the remaining wires and connector with WD 40 and put two cable ties around the connector to hold the two halves tightly together, that was approx 2 to 3 years ago never had the problem since.