If it's anything like my '83's headliner, it is separating because the
foam padding is failing. You end up with one thin layer of foam on the
fabric, and one on the cardboard backer. I've also been told that to
repair it is nigh on impossible; you have to scrape all the old foam off
both surfaces without damaging either in order to have any hope of an
adhesive sticking and holding for very long. Maybe it's easier with
leather than with vinyl...

(I haven't had mine repaired yet; this is one of several reasons why my
V6stang has been parked for a good long while)

\         ~~ Ventis secundis, tene cursum ~~          /

I redid the headliner on my '86...  It was vinyl, but hanging down all over.
I got some cloth velour material from one of the mustang places.  A little
bit of a PITA to get the old foam off, but now that it's in it looks better
than new.  I like the velour better than the vinyl.
A decent upholstery place should be able to get you the right leather
pattern.  Biggest issue is the backer board, be careful with it.  Use a wire
wheel and a light touch to get the old foam off.  A little 3M adhesive
spray, and lay the material on.  Use a roller over it to make sure it gets a
good bond.  Leave plenty of extra material around the edges, trim after you
get it in place.  Took me an afternoon, and I had a sunroof to contend with.
mkl

My dad just had to get his headliner replaced.... the summer heat
around here causes them to delaminate fast. Not sure but I think his
came from JC Whitney (not my first choice, but ya gotta do whatcha
gotta do.\).