If the Third brake light is the only one working , it sounds like the multi function switch...aka turn signal switch...Just had the same problem with my 98 cargo van..
On a 1996 Ford E-150 : Rotate the headlight knob in your dash fully COUNTERCLOCKWISE to turn on the courtesy and cargo lights
probably the sensor
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The alternator is weak or the belt is slipping.
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loose wire?
It is located on the Left Side ( facing the engine) by the Alternator.
Remove the instrument cluster.
Check fuses under dash on drivers side. Jeff turn siginal fuse ok?
On a 2006 passenger van the lights will go out after several minutes on their own. There may be some way to change that in the computer...?
Wear on either the bearings or race.
I have a '95 E150 and a '96 E250, both are 4.9 straight 6 cyl. One has 1 O2 sensor and the other has 2, one on each half of the exhayst manifold. I believe the 96 has 2. but it is an E250, not sure about the '96 E150.