Astronomically speaking, dawn lasts about 70 minutes at the equator, with dusk lasting just as long for a total of 140 minutes of some form of twilight (the equator being the area with the most consistent, and shortest, periods of twilight).
At the equator, the Earth will be relatively moving at its fastest, at about 1,000 miles per hour, or 16.6666... miles per minute.
The combined width of all twilight at the equator is thus = 140 minutes X 16.667 miles / minute = 2,333.33 miles.
The equator is about 24,901 miles in circumference.
The percentage of all twilight that covers the equator is thus = 2,333.33 miles / 24,901 miles = 0.0937 , 0.0937 X 100 = 9.37%
So: a little more than 9% of the area with the shortest period of twilight is experiencing twilight. If you say only civil twilight counts, it comes to about 3%.
I'd guess that this percentage is fairly constant throughout latitudes, as while the periods change, the total amount would even out over a year, but I can't be assed to do the math.
