It sounds just like valve noise, but the valve cover itself is as quiet as you'd expect.
Here's some reading on removing the tumble flaps.
If you want your car to be stock again, then you should purchase a new intake manifold, or a used intake manifold without the damage. Now my car has been making tumble flap noise for about 50k miles now. It started around 100k. I knew what it was, and how to fix it, and I knew I didn't have what I needed. Now I have what I need, but no time to do it in. As soon as my 3rd vehicle is repaired, then I'll be able to put the ZXW up for a while and repair it.