UPDATE:
It seems that this problem may have come from a faulty ground wire.
I brought my 2003 ST1300 to the dealer, and they replaced the subharness under safety recall, and did say that my ground wire was bad.
Immediately, I noticed the headlight sticking quirk had been resolved.
Today, the fuel gauge responded properly by dropping down to one, blinking tick at 1.3 gallons remaining. My fuel miles-per-gallon has ascended to normal with a new thermostat.
I'm not going to shut the door on this entirely, as Kempo claimed that he has this same problem intermittently. It could happen again. For now, I've decided it may be a good idea to carry an extra quart of fuel with me just in case... :nuts1: