Previous owner cut out a piece of the glove box to install gauges were the radio was initially located.
I want to use the glove box from a later model (smaller) to replace the missing piece.

Any idea how to attach it into the glove box (fiber glass, glue, ...)?

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There's a strap that's supposed to be inside your dash that holds the glove box in....

Yes, I still have got the strap but want to cut out the missing piece from one glove box and "glue" it into the other one.

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you could ue some fiberglass patch epoxied on to the outside surface once you cut the replacement patch to size. I did this to strengthen my pedal board.
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Why? Seems like a lot of effort. Is yours an early model and you can't located the wider box?

No, to install I need the early, wider one with the missing piece and I have a spare, smaller one.

I would post a WTB in the classified section to find an early glove box. I would think someone might have one available. There is a FS ad in the classified now for a full 71 part out. Contact the seller and see if he/she has one.

I have used shellac as a binder, along with epoxy, acrylic, and white glue. It is paper mâché no mater how you slice it.

I hate installing these things though. Don't make it too inflexible.