I think the underneath part is actual wood, but the strip that's coming off it is plastic or vinyl. Also, if the glue requires a long curing time, how could I best apply horizontal pressure?

Just about any contact adhesive from your local hardware store will work fine.
Or something like liquid nails construction adhesive.

For pressure, either put something heavy against it (books will probably work okay) or if there's something nearby directly opposite the loose strip, just wedge something between them so that it bears on the face of that strip.

Don't use a mastic like liquid nails. That's a terrible idea. A few dabs of caulk and then press the board in is not ideal, but better than putting a fucking rock behind that veneer. Rubber cement would be way better. Specifically the type used for veneer. Shit, 3M spray can adhesive would be not so bad, either.

>>2920296
Thanks. Smart idea for how to apply pressure.

>>2920299
But you think contact adhesive is all right? What about Gorilla Glue?

Try reactivating the glue with an iron.

>>2920303
Gorilla glue expands and foams. Professional laminates use contact adhesives. 100% silicone might be my second choice. Super glue gel would probably get the job done.

>>2920292 (OP)

>>2922478

>>2920292 (OP)
Make a third thread for the correct answer asshat.

>>2920292 (OP)
>what kind of glue is good for wood
gee I wonder.