Because of the limitation of 256 colors and the large file sizes of animated gifs that can only be viewed with your favorite browser, I think even a resolution of 1080p would not work well.
I think the best way to do an animated or cinemagraphic image is by shooting it on video first. Although the following doesn't exactly fit what the OP was asking about, here's a quick example I did.
I opened a 1080p video clip I shot some time ago in a video editor, Vegas Pro, in this instance and selected 3 seconds that I thought would loop well and rendered it out at a resolution of 480 x 320 at 30 fps. I then imported that 3 second clip into Photoshop and chose to use every other frame. That gave me a total of 50 frames for the clip at 15 fps. I then saved for web as an animated gif that looped forever. This 3 second clip wound up having a file size of 3.7mb.
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