[Bike...and Dennis]

I had some similar doin's. It was the plug at the top the starter relay. Many of them heat up and melt. Honda finally made a fix-kit for it I've heard. Under warranty, the dealer just soldered some spades on the wires and replaced the relay. That was 24 or 25 years ago and it's still working, so...
Another possibility, is simply a loose or dirty plug somewhere in the main power supply. It's not as likely though.
As far as the dogbone fuse. You can buy new ones. I've never had one fail in 270,000 miles, though.

 

[Bike...and Dennis]

Pulse gen, as UbarW mentioned, or its circuit, wouldn't shut down the lights. The switch and the plug at the top of the starter relay are both common GL12 maladies.

Something I just thought of is...if you lose the clock set and radio memory, it's more likely the relay. If not, then the switch is the better choice.

 

[Bike...and Dennis]

Harris.
You should really open a new thread for this, as it's a different issue. Meanwhile, clean the starter switch. Open up the switch housing and spray behind the button with WD-40 while pressing the button about 1,000,406 times, give or take a million.
Another possibility is the high/low switch. Next time you go dark, flip it to see if anything changes. The only thing is, those common maladies don't usually affect the dash lights.
Also, replace the light fuses in the fuse panel. Not the main fuse. It has nothing to do with this.

Oh, and welcome to the forum.