Yeppers, been there too. I ran out about 10 miles from a gas station, right in front of a most sketchy land-grant community. (Predates the US and doesn't entirely recognize federal -- much less state -- authority.) But before I could finish being upset, some very nice Nortenos stopped on the freeway, gave me a ride to that gas station, and then back. I filled their car with gas and gave them the gas can.
This is an easy fix. Search here on "Mustang" to find a Mustang PN that crosses perfectly, available everywhere. (I think it's in Dollar-to-Dollar too.) Take off the seat, unscrew the sending unit (top of the gas tank), and pull it out. Unplug it, let it dry, and swap out the indicator-light sending unit (need a solder iron) -- the gage sending unit is on the same stalk. The new one will tolerate getting soldered back in. Didn't fuss with insulation, just put it back together in a way that the wire connections won't screw up.
I don't really know whether my dash light still works because I totally quit pushing it.
Twice, in work rigs, I ran out of gas on rather desolate stretches in NM ... but just happened to be close enough to coast right up to a gas pump. But y-all already know I was born lucky.(Well, one other time, not quite that lucky.)
And yeah, it's swell that these bikes come with manual control for the gas mileage -- located on the end of the right handlebar. Mine gets low 30s at 80+, but mid 40s at 70-75. Shot up to high 50s on the Natchez Trace (50mph).