Originally Posted by
mvoight
Interesting, under 8 minutes costs more than 8 to 30 minutes
Probably to use it as a toll road instead of going to a terminal

Yes, driving through the airport is more direct that the circuitous route that they want you to take (114 to 121 to 360). So originally the under-8 minutes toll was to deter people from taking a shortcut through the airport.
The pricing used to be a toll for under 8 minutes, free between 8 minutes and an hour, and a toll for longer than an hour.
I don't remember when it changed to 'pay a toll no matter what', probably when 95% of new roads built in Texas became toll roads.
OP - there is no cell phone lot AFAIK, but I have often seen people parked on the side of the road prior to the toll gates. Probably not the smartest move just to save a dollar or two... All the terminals have short-term parking (1 hour) very close to the entrances.