Oh, those were may a couple of years ago, so I don't quite remember every detail.
They have 120 frames (compared to the 360 of the original). That keeps the animation of the thumbnail smooth enough, without unnecessary data.
(Your #24 one seems to have to many frames, causing the browser to have trouble with it. (It looks good when I run it in the export gif preview in Photoshop)
(And the #23 one has to few - so the animation is too stuttery.
When generating the gif of a particular animation, I used prepared color palette files (.ACT) for the gif creation in the export options of the video editing program (Adobe After Effects).
Those were created in Photoshop. Done by opening one of the frames in PS and reducing the color to an indexed mode (instead of rgb). Then the color palette could be saved as an ACT file. That ACT file could be used in the video editing software in the GIF export options. - That way I could experiment in Photoshop on how low the number of colors could get and still have it look good. - Although i think this was only necessary because of the limitations of the the gif exporter in AfterEffects back then - it may not be an issue these days...
Well, in general, try to keep the number of colors as low as possible and experiment with the options (like "adaptive" and "diffusion" and dither and whatever else...)