There are different ways to anchor into thin material.
If you have access to back side, a piece of wood is great and would be strongest as it would spread the weight over a larger area, basically the size of wood.
If the material is inaccessible on back, then a toggle, molly or perhaps a zip-it(screw in anchor) or even a plastic plug mentioned above, would be ok for drywall, I don't recommend either for less than 3/8" material unless what you are fastening is light weight and doesn't need to move.)
After wood backing, toggles would be your next strongest, you just need to watch the depth.
Molly's come in various lengths including the thin material that you are working with, just be real careful not to strip them!
With what you are securing, just a light weight monitor panel, any of the above methods are sufficient.
I just saved time and found a page that will explain some anchoring methods...
Pictures and info on thin wall fasteningGood luck!