I shared my $.02 because of experience with this very same issue. This is not from someone that is simply overly cautious.
Went to work (only 7 miles to the office). I knew I still had 25 miles to go, since I was at 75 on the trip meter since last fill up.
I did not pay attention that there was an accident on Rt 3 East. Backed up traffic for miles. Could only move about 3 - 5 miles per hour that morning. Everyone that took that road was late getting in. Took almost an hour, for a normal 12 minute ride.
When heading home, I got about 1/4 mile from the office and the bike started stumbling. Did not see a low fuel light, but still flipped it over to reserve,, just to make it to the Mobil station before hitting Rt 3 West to head home. Got NOTHING!!. Checked the tank, It was completely dry.
Had to get the late shift guy to take me to the gas station and find a container that I could put some fuel into AND convince the fuel attendant that I was not using that container for something illegal, and that I would be right back with the bike to fill up.
That weekend, pulled the tank and sender out. The sender itself looked OK but running resistance check on the wires did not check out correctly.
Ordered a new one, but out of curiosity, I cut the metal can on the sender open.
There is a little thermistor (Resistor that is sensitive to heat changes), that is soldered to one lead of the sender. In normal operation, it gets warm, when removed from the cooler liquid fuel. This, in turn allows a circuit to cut off power to the fuel pump and illuminate the low fuel lamp. Flipping the RESERVE switch bypasses the cut-off circuit to the fuel pump, but leaves the Low fuel light, illuminated. (I actually took a picture of the corroded thermistor. If I can find it, I'll post what it looks like inside that sender unit).
Well, the old sender had rust inside the little brass can, and the rust corroded the Thermistor so bad that it did not pick up the temperature change, when not submerged in fuel. Since then, I've coated my tank to eliminate any rust build up.
Because of the traffic jam, I used way more fuel, moving slow, but got no warning of this.