How to implement animated sprites in UI Components?

In essence what I want to do is take an animated GIF and use it as the source image for a UI Panel for a title screen. Since I’m well aware that Unity doesn’t actually support animated GIFs naturally, I separated the GIF into its separate frames and tried to create an animation for it. While I was certainly able to create an animation for it, though, the animation only plays in a sprite renderer component that gets placed into the panel and therefore doesn’t actually do anything. What I want to know is how to have the animation that plays in the sprite renderer play in the Image component’s source image.

I’m well aware that I could do all this with script if I absolutely have to, but I’d rather try some non-script options first since it might make things easier with more complex animations.

There isn’t any Image animation support currently that I’m aware of. It’s a part of the 2D framework that isn’t implemented in UI.
But that sounds like an awesome proposal for a new control in the Unity UI Extensions project (link in signature)