Still texture/pattern on a moving object

I’m looking to do something similar to how characters are animated in Chowder. They have a stationary background for their clothing, which does not move with the character. Similar to how the lens of truth works in Zelda.

In other words, I need an object to reveal part of a layer as it moves over that layer.

I’m not exactly sure what you mean, but are you trying to make the background stay in place or… Could you show a visualizing of your game so far so we can see what you mean?

Have you looked into the masking function?