I think if people wait until the last gallon in their tank before filling up then they'll save more money on gas over time. There will be fewer total fillups per distance traveled and there will be fewer times when the gas cap is popped off and vapor lost at the gas pump. Economy in gas vapor savings increases as the driver gets closer to zero gallons left in the tank; a risky strategy if you guess wrong or if a gas station you were counting on is closed or out of service. In a populated area where there are lots of fillup options, a thrifty driver should always wait until the tank is almost empty before filling. Waiting until there's one gallon left is enough to ensure you find a station.

The gasoline vapor inside a gas tank is at the same pressure no matter how much gas is in the tank--there's always the same amount of gasoline fumes per unit volume of empty space in the tank (assuming the same ambient temperature and weather conditions.) I believe your point is that the gasoline liquid gives up a greater percentage of its volume the lower your tank gets. One gallon of liquid gasoline has the job of filling the rest of a 12-gallon gas tank with fumes whereas eleven gallons in the same tank only have the job of filling one gallon of empty space with fumes. This picture of the process ignores the fact that the eleven gallons already DID fill up the one gallon of empty space with fumes. The last liquid gallon doesn't have to fill the whole tank with fumes--it's already filled by previous gallons.

If a 12-gallon tank in a 20 mpg car has six gallons of liquid gas and six equivalent volume units of gas vapor when you fill up, you'll lose six "volume gallons" of gas vapor at that fillup and sixty volume gallons of gas vapor in 1200 miles of driving (120 miles per half-filled tank and ten half-fills to get 1200 miles.) If you wait to fill the tank when there's only one gallon left, you'll lose 11 volume gallons of gas vapor in one fillup and the same sixty volume gallons in 1200 miles (220 miles per eleven-gallon fillup, 1200 divided by 220 = 5.45 fuel stops to go 1200 miles. 5.45 x 11 = 60.) In short, you lose the same amount of gas vapor from the tank no matter how often you fill up, but the filling-up process loses vapor in and of itself. Vapor is lost to the outside air each time you open your gas cap. Minimize your gas station stops!

I don't believe this is true because petrol fumes aren't caused by agitation. The speed of the flow doesn't have anything to do with creating fumes...they happen because of the evaporative nature of fuel, and the relative density of the atmosphere above the liquid.  Actually, speed DOES have a lot to do with it....the faster you can get the fuel in and whack the cap on the tank, the less is going to evaporate into the atmosphere! So I actually believe you should do the total opposite of tip 2!