I would have persisted in getting the two parts of that (White) connector apart personally as it is the supply to the headlamps and instrumentation among other things.
I went through a week or two of my headlights just dropping out on me and losing instrumentation, but a quick turn of the ignition off and then back on again brought the lights back and returned instrumentation.
I don't ride at night so I was not unduly concerned, but, when I went away on holiday I relied on the bike as it was my only transport whilst away, and riding down a narrow lane with passing places on night I had just rounded a very sharp left hander (Complete with gravel on the crown of the road) and was thrown in to total darkness, fortunately I did not know the road otherwise I may have been pushing on, but, as it was I was doing probably doing less than 20, and as the bike was upright I just slammed on both brakes and stopped fine, albeit totally blind.
I had to be rescued by following a 4X4 to civilization, bike was still rid-able just no lights or instrument.
On arriving home I checked all the usual things battery connections, all connectors under the seat, wiggled the ignition key, popped the fairing infill panels off to check the connection at the headlamps and all seemed to be
fine but still no lights.Standing there with my hands over the left hand side of the fairing thinking rude thoughts to myself i touched the infamous large with multi electrical connector, and low and behold the lights fired up, wiggled it again and out they went, I did this a couple of times just to convince myself I had by luck found the fault.The two halves of my connector wanted a lot of encouragement to let go of each other but when they did it was instantly obvious that a number of the connection halves had corroded away and were only making contact intermittently.I cut the wires tight to each half of the connector (Colour coded so all good, but take a photo with your phone just in case) slipped a 50 mm length of shrink fit over one half of each pair, bared 15 mm off the end of each wire twisted them together inline and soldered, then slipped heat shrink over joint and gently heated the shrink with a fag lighter (No I don't smoke) and jobs a good-un. That was 2 maybe 3 years ago and have never had a problem since.I have heard that this is quite a common fault with these push fit connectors if that are in a venerable place IE: under the infill panel on a Fazer FZS 600. especially if you are a bit anal about washing and polishing it (Me Me) or the bike is out in all weathers. I guess thinking back I repaired about 4 maybe 5 pairs of wires, the others were ok.Cable tie around the connector pulled up tight after a liberal spray of WD40.Until that happened I never really understood when someone said that something frightened that much they could have crushed a walnut between the cheeks of their arse