The question I have is will the starter relay stop all electrical power to the lights....
That RED WIRE which plugs into the starter relay powers the fusebox, and then from there, all things which branch off from the fusebox. Yes, in-between there's the ignition switch but the red wire is the original +12 tap. If the terminal on the red relay wire is toast the symptoms mimic a bad main fuse, but then the lights, etc, goes on again by its own self. Then off again. Be grateful that the faulty terminal doesn't shut off the power while you're in the middle of traffic. That can be bad. Perhaps, the alternator provides a surplus of power while the bike's in motion that's sufficient to power the bike through the electrical connection that's hanging on by a thread. So, the bike only dies when you stop. Dunno know the mechanical reasons, but it's been good e'nuff for me.
It's probable that if the red 4P connector at the relay is bad, that the 4P connector at the other end of the same red wire is toast too. That other 4P connector is white (translucent) so it's easier to detect visually the telltale burnt marks. It might be worthwhile to check the second 4P connector. How about the 2P connector on the alternator/RR? R J's suggestion of replacing the red relay 4P connector with the Gold Wing kit is right on the mark (photo above). Even if the side clips on the red 4P connector are passable....enough to grasp the starter relay, which they probably aren't....the plastic material is now so brittle that the partitions between the individual internal sockets have literally fallen apart. The female metal terminals don't seem to remain securely on the prongs without the aid of the red cover. Meanwhile, here's a diagram I drew up to illustrate how the RED WIRE at the starter relay serves as a main electrical artery. Arrow denotes direction of electricity.

As with all things Internet, don't rely on my words alone....

the fuse connection from either water or loose connection has caused it to overheat....
That's what I'm thinking also. Probably water from washing.