I looked at the first result of the search you linked to and I don't agree with it. It mentions aerial navigation, but I think the phrase originated in what pilots call stick-and-rudder skills.
When you turn an airplane in flight, you have to coordinate two main controls: the ailerons, which make one wing drop and the other rise; and the rudder, which makes the plane rotate on its horizontal axis. If you don't coordinate them correctly, you feel your bottom -- the "seat of your pants" -- pull to one side.
An instrument called the "turn coordinator" displays this for the pilot. If the turn coordinator fails, you have to fly by the seat of your pants: by feeling in your rear end when you need more or less rudder.
By extension, any time you rely on more fundamental skills to get through a challenging situation, you can say you're flying by the seat of your pants.