I recommend opening your GIF in Photoshop, where you can adjust the color palette, resolution, and number of frames. Once you do that, you can then drag your image into a tool like Imageoptim.
Here's a nice set of tips: https://design.tutsplus.com/tutorials/10-ways-to-optimize-an-animated-gif-file--psd-34649
Essentially you're balancing a few things:
- Frame rate
- Number of colors (out of a possible 256)
- Length of animation
Make sure you don't have any frames that repeat -- that can add a lot of additional weight.