Craig, your dash pad (it is probably a replacement pad) is suffering from sun and age hardening and the ends will tend to shrink, if you will, and pull out. Really not much you can do to correct this. Getting that thick vinyl to lay back down is not going to be doable. A fix that seems acceptable is to lay in a piece of matching vinyl patch, perhaps folding the edges over to look finished, and tuck and glue this in place, like it was supposed to be there. May have to use your imagination . The only sure-fire fix is to replace the whole sheebang. This ain't easy as it entails removing the windshield frame and lots of stuff below it. Good luck.
Bill
Oh, and to answer you question, 3M black adhesive in a tube.