What is the rear trunk board made out of? I need one

If your talking about the mat it is foam rubber and perlon carpet.

This is the pad I am referring to. What is it made of?

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rubber mat. 45 year old rubber mat.

These trap water under them.

I don't like them.

It is foam rubber.
I bet you could make one from Masonite and it would do two things..
A) even out the carpet as the original does
B) let air underneath so it won't trap water like the original does.

Might be worth a shot.

Later cars had a particle board that was sealed in a plastic pressed "she'll" for lack of a better term. I would look to salvage mine by carefully slitting it at the edge of the seam on the bottom.
Make a pattern from the plastic about 1/4" smaller and you should be able to insert and glue back together. Would make a great thread.

Foam rubber. It's purpose is insulation from the heat of the muffler.

Later cars had 1/2" foam encased in black plastic that covered the whole trunk.

The rear trunk leaks enough through the seal or the tail lights that a stuck on solution is inadvisable. Carpet that you can pull up after a wash is nice and would deter paint scratches and keep the tool bag of spares from sliding too much.