Tailpipe Charlie

I had lived in Taiwan for several years representing several American companies that did business there.  Taichung is in central Taiwan and accessible to the whole island within a 2 hour drive.
 On this particular day, my boss from the USA and I had visited a factory south of the city and were returning to Taichung in the late afternoon via the north/south freeway.  There is a Taiwan Air Force base near the city (CCK) that was formerly used by the US as a base for flying supplies to Viet Nam, and the freeway passes directly beneath the final part of the landing strip and the ocean approach.  The planes on final cross the freeway perhaps 400-500 feet above the ground at this point.  The landing strip itself has two parallel runways and it's common for fighter type airplanes to land 2 at the same time.
 As we approached the flight path area, two F-104G fighters were crossing the flight path directly in front of us preparing to land.  Directly behind one of the F-104's was and oval shaped object, about the same length as the F-104 (maybe 30 feet long), dull silver in color and perhaps 10-15 feet thick at the thickest part.  It was perhaps 10-15 feet behind the tailpipe of the airplane.  
In an instant, the object flew off at a right angle, and as luck would have it, directly in my line of sight.  It just got smaller and smaller and disapeared in an instant into a clear sky with good visibility on the ground.
 I'm pushing 70 now and haven't mentioned this experience to anyone since I saw it, since I didn't want anyone to think I was a nutcase.  
I've had a life long interest in aviation and earned a private pilot license back in the early '60's.  Because of this, I watch the sky a lot and see many things that others don't see.  
I've had another sighting in the sky over Los Angeles that I'll write about some other time.
Witness indicates that the date of the sighting  is approximate.  PD