The insulation melts when the wire gets too hot, and that is usually from pulling more current. The red/wht wire is only half the current pathway. Current needs to return to battery in some way and that is usually the Green wire path. Check all the ground connections and wires.
Overcurrent can be caused by a faulty rectifier, or (even Momentarily) reversing the battery leads, turning all the rectifier diodes fully into conduction.
Of course, with the fuse by passed, overcurrent will seek out the weakest pathway to turn into a fusible link. Let's see, by pass the fuse, short the wiring someplace on the bike and ... poof.
And, the wire itself may not be ok. Multistrands, can melt or part only some strands. Can't really tell without looking at them all. They can part at the crimp connections, too, leaving less strands to carry the current loads.
Cheers,