2D: Irregular shaped window to another world?

I want to make an irregular shape display its colors from a different set of images. Currently, I have a flashlight represented by an irregular shape (kite shaped) that when casted over an area, certain objects appear. When the shape is removed, the items disappear. Now, I want to have the background that is within this irregular shape to display an altered version of the background.

I am planning to use a RenderTexture to get its info from a camera that views the flashlight's corrosponding location in the other world, and then use this image as the basis of the flashlight's altered background. However, when I try this, the flashlight shows black instead of the other world. When I texture a plane, the RenderTexture works properly. Anyone have any ideas how to accomplish this?