(See the best response by Kaiochao.)

In my game I have a series of objects which are just icons that essentially act as an overlay without being attached to anything specific. (Think like shadows or colored lights) My problem with these objects is that they remove my ability to mouse over or click the things underneath them, which I still want to do.

Is there a way to force the mouse to ignore their existence?

Best response
mouse_opacity = 0

(Refer to the reference for more info)

Actual overlays/underlays won't work with this, I'm pretty sure.
Perfect, that's what I needed. Much appreciated.