No don't remove the fairing at this stage, look under the tank in the black box full of connectors, or, under the Clutch Lever (Left hand side as your sitting on the bike) side front fairing infill panel, 3 screw to access that one so I would check that first, switch ignition on and the headlights and wiggle the large white plastic connector that under the front fairing infill panel, if the lights flicker on and off you found the problem in the connection box, if it does not make any difference I would check the black electrical box under the tank.
let us know how you get on.