How can I make my desktop wallpaper image an animated GIF?
You can use Mojave's dynamic wallpaper. macOS doesn't natively support animated GIFs as wallpapers.
However you can use this https://lifehacker.com/set-an-animated-gif-as-your-macs-wallpaper-1756859302 but at the cost of a shorter battery life for a wallpaper that you probably wouldn't see in action because you got windows all over.
Your case is more like needing a really thin phone(GIF) which you are gonna cover with a case(windows) anyways.
You can also use this tool to set animated GIFs on your desktop: Bionix Animated Desktop Wallpaper
I'm afraid OS X does not provide for animated wallpaper. There are some apps that claim to do this such as DeskFun and BioniX.
As yet another free alternative to run GIFs and APNGs as desktop wallpaper I wrote the screensaver AnimatedGif. It is complete Open Source and can be found on GitHub.