After years of reading others' misfortune with total electrical failures, it happened to me today. Fortunately it wasn't in the middle of nowhere and I managed to sort it and limp home.
Inside the rubber boot forward and left side of the carbs there's a cluster of electrical connectors, including a couple of red ones. One of these is a 2-pin connector taking power to the ignition switch. As you can see from the photo, mine had severely overheated to the point of melting the connector block and the wire insulation.
I'm going to replace the connector and damaged wire tomorrow but I discovered from another old thread on the FZ1OA that one of the red wires leading to the connector is actually the feed from two red wires which are crimped together further back in the loom. Apparently, corrosion or dirt in this crimp can be the root cause of the overheating so I'm going to check that, too.
Might be worth taking a look at yours next time you have the tank up.