Anyone looking for just about any job in the government (including an AF FTE job) should become familiar with the USAJobs Website (
www.usajobs.gov/). It is THE portal for employment. When a job announcement comes out it is posted to USAJobs for a week or so. You can set up a filter on your account so that you get notified by email when a position you may be interested in comes open.
One of the people I work with did exactly what you are thinking of: He flew tankers. Got out and decided to be a full time engineer. He says he couldn't see being a commercial airlines "bus driver."
Getting into the USAF TPS is very, very difficult partly becuase it is so competitive. Basically, if you don't have a master's degree you are not competitive. You do not have to be a test training school to be an FTE. Most of us got to where we are with OJT.
I recommend you dive in and get a feel for the water!