The plastic I used was a sign-maker's material - like the kind they use for the ad panels on the outside of city buses. It was a left-over from a sign at our church from a Billy Graham Crusade. It was my job to remove the signs. It is a solid sheet somewhere around 1/16" thick and can be formed using a heat-gun, but is resistant to lesser heat and moisture.

I made mine using 1/8" thick Masonite, with black vinyl adhered using spray adhesive. 

Thank you Dan, it had already been poorly recovered, so perhaps not worth the effort. at least its a pattern.

About the only way to flatten a bare card is to moisten it very gently, then press it between 2 flat surfaces, e.g. sheets of plywood, with a lot of heavy weight. Leave it to dry - the plywood would absorb some moisture. If you have sheets of smooth felt or a flannel sheet, it would help absorb and dissipate the moisture.

If you are recovering it, then it is no longer an "original" part. Since the card is not visible when installed, I'd replace it, possibly with a thin sheet of plastic the same thickness.  It worked well on my dash cards. With the horizontal parcel shelf, I was able to pre-form the plastic to make the arch over the switch panel section before putting vinyl on it.

Any good ideas on how to flatten a wavy rear parcel shelf? The material is stripped off, just the card, need to get it flat, before recovering. It's an original 62 part I would like to reuse. Thank you.