Hi Customer, I am John Mc, a Ford dealer technician.I hope I can help solve your problem quickly and accurately.
It sounds like you either have a worn or broken reverse band or the seals for the reverse servo are bad. This is a completely hydraulic action so no electronics are involved. I would try replacing the servo seals first. You can pick these up pretty cheaply at a dealer. To replace you remove the pan and remove the reverse servo. It is inside the trans and is held to the trans case with 4 10mm bolts. Remove the cover and remove the piston. Now replace the seals on it and reassemble. If it still does not work you will need to remove, disassemble and repair the transmission. This is a fairly complicated transmission so I don't suggest trying to do this one without experience. To get access to the band the trans has to be completely torn down.
If you have any more questions please feel free to ask, it's what I'm here for!
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The filter is right inside the pan and will be very obvious. It is held on by a 10 mm bolt.
Here is a pic to assist you, I'm highlighting the reverse piston. The seals are o rings that go on the piston.