Had a horrendous rattle start up in my 88 vert. Turns out to be the inside panel on the Targa top rattling against the outer.
How is the inside panel secured into the outer one? I see a PO has put a self tapping screw at each front corner.

 

It's held on by plastic push-pin fasteners. So take off the trim on the side (it's glued on with some really gooey adhesive, just pull it off) and pop the headliner off with a trim tool, putty knife, or even a flat blade screwdriver. The push pin fasteners can be bought at most parts stores in the aisle where they carry the "HELP!" stuff.