Did you get your problem sorted out? Just in case you didn’t, here’s my two cents.
From the picture of the wiring harness in your other post, I made some assumptions and prepared the attached schematic diagram. The diagram shows my conception of what I think your harness looks like, plus the rest of the headlight circuitry in the FZ6’s electrical system. This diagram assumes that you installed a second H4 bulb so that you would have two high beams and two low beams. When the problem occurred, did both sides act up at the same time? Did you attempt to switch from low beam to high beam, if so, did it work on one but not the other? If it affected both sides at the same time and neither high nor low would work, then the problem must be in a part of the circuit that can affect both sides and high and low at the same time. Possible suspects include: the connection from the headlight relay (the relay that is part of the bike’s standard wiring harness, not one of the ones in your harness) to the headlight fuse, the connection from the headlight relay to the ECU, the connections from the factory low beam plug to your wiring harness, relay no. 1 in your harness (as indicated on the diagram), the connection from relay no. 1 to relay no. 2, and the connections from the harness to the battery. Since most of those possibilities are within or connections to your wiring harness, I would remove it, reconnect everything as stock and see if the headlights work. If they do, then the problem is within the harness. If they don’t, then it is most likely the bike’s factory headlight relay (as I believe Wrightme43 was suggesting.)
If relay no. 2 itself, the connections from the factory high-beam plug to your harness, the high beam bulb connections to your harness or the handlebar high/low beam switch went bad, then the high beams would not work but the low beams should. So if your low beams are working when it acts up, check these areas.
If the low beams don’t work but the high beams do, the problem must be in relay no. 2 or the harness’ low beam bulb connections.
Hope this helps. If not, or if I was unclear (I have been accused of sometimes providing too much information), feel free to ask more questions.
Jeff