I ordered my foam from a guy who makes pre-cut, ready-to-install kits for the air boxes for classic/vintage muscle cars and just used quality 3M spray adhesive to lock it to the box. It's the same kind of foam (density and all) as the original used on our boxes, pretty cheap too at I think $5.00 a sheet and 1 sheet is really all you need to do the air box. If you like I can send you some pics I took during the process of fixing mine.
The foam tape that Cre was talking about will work very well for the ductwork joints and such (and there are quite a few), but probably not so well for the panels and doors on the interior of the box. The control mechanism doesn't seem to have a lot of free-play to allow for any additional thickness of the seal which you'd likely end up with going with the tape alone. But for use on the joints, absolutely.
Here's the website for where I sourced the foam sheets from....
http://www.detroitmuscletechnologies.com/
Real nice guy to deal with, very helpful. Either call or email (and he responds well to either). He inquired if there was enough interest out there to justify making up a kit for our MkIII's, but given that our dash's aren't the easiest in the world to pull and we only do it when we HAVE to, I couldn't tell him that there was.
Good luck with yours in any case. Oh, and one more warning.... DO NOT BREAK THE DASH MOUNTING PINS UP NEAR THE WINDSHIELD WHEN YOU PULL THE DASH! They're tricky, they're just plastic and they aren't available through Toyota anymore (though the receptacles are) unless you buy an entire dash. So finding someone with replacements will be your only option if you do. Pull upward gently on the dash when you've got all your bolts/screws/wiring plugs disconnected.