It looks like this is indeed an issue with the mesh itself being a collection of one-sided planes. And, as mentioned previously, due to the normals, they can only be seen from one side.
You have two solutions to this:
The better solution is to duplicate all of your single-sided planes, and then simply flip their normals. That way, you have 2 planes on top of each other, one facing up, the other facing down. No matter which side you view it from, only one side will be visible.
The faster solution is to apply $nocull 1 to your material VMT. This will cause both sides of the one-sided plane to render, but lighting information will only be received from the “correct” side. Depending on your use application, this might be fine, or it might cause severe lighting oddities. For a prop this small, I think you’d be fine, but it’s still worth noting why this idea isn’t a catch-all solution.