Look up mounting to EIFS.

I'm just spinning ideas here based on the information I'm seeing, but...

The client has to know that mounting ANYTHING to this will damage it permanently. That won't matter behind the camera mount, but it will matter in ten years when they want to do something else. They need to think of the new owner of the place when they sell it, and what these damaged wall areas will do to the sale price. And, hell, the neighborhood!

So the outside is essentially styrofoam and you have to go quite some distance through it before you reach material that will support what's mounted.

Assume you've got the screws worked out. You can't just take a normal mount and bolt it to the wall. Properly tightening the screws will put so much pressure on the outer surface that it will collapse, leaving you with a loose mount and styrofoam that will just get worse over time.

What you'll need to do is spread the pressure exerted by the mounting screws over a larger area than the camera mount. Let's say your mount's area is about the same as a 2 gang electrical box, about 4" x 4". Make a back plate for the mount, say an 8" circle. (Yes, this is ugly and sure as hell not subtle!) Arrange a half dozen or more screws around the outer edge of this plate and tighten them only until the plate is snug on the wall. You MUST NOT crush the styrofoam AT ALL! It will help in the long run to use some glue on the back of the plate, too, as that will stabilize the entire plate better than just screws.

That's what I'd do, but I'm just inventing this on the fly. The sources I found when googling "mounting to dryvit" were my starting place. There are probably better ideas out there.