I've noticed that when the tank is down to 1/4 capacity or less, the fuel gauge will occasionally go down a bar, then back up again. Yesterday it went from 2 bars to 1 (triggering the low-fuel light) for a couple of minutes, then returned to 2 bars (light went out). I was on my way to the gas station anyway, so I wasn't too concerned.

Something even more interesting happened a couple of weeks ago on my way home from work. The gauge dropped to 1 bar (triggering the light), then about 20 miles later the last bar disappeared. Since I was only ~15 miles from home, I decided to do an experiment. I pulled into the nearest station and put in exactly 1/2 gallon. About a mile after hitting the road again, the gauge suddenly popped all the way up to 2 bars! (Next day I refilled the rest of the way at a nearby station where the price was 7 cents less.)

Has any other '05 HCH driver encountered this or any other kind of strange behavior on the fuel gauge? Is the mechanism used to estimate remaining fuel simply unreliable at low levels?

I've seen that happen in my car. I've driven 20 miles with no bars. I think once the fuel light comes on you have about a gallon of gas left, since you're averaging about 50 mpg you won't need to worry about it right away.

I have noticed many times that once the fuel gauge gets to 1 bar the light comes on and then after a few miles depending on whether or not I'm going uphill/downhill, I'll get 2 bars to show and the light goes off.

I think its because what little fuel is left, 1-2 gallons, is sloshing around in the tank and confusing the sensor. Probably need to do this experiment on level ground, if you can find any. Not sure, but I dont think its a good idea to run the tank to almost dry because of the stuff that may be lurking at the bottom of the tank like water/condensate.