Disclaimer: There might be a way to do this properly but at least with the tools I used, lowering colors didn't seem to help, probably because it creates additional changes between frames.
I got this idea while responding to #299.
Background: I use ScreenToGif to help demonstrate short processes and for writing up bug reports, frequently I don't need precise detail to explain what I'm trying to do. Currently ScreenToGif saves to the 256 color standard. With fewer colors, I think you might see file sizes decrease.
I tried to put together a process to demonstrate how taking images recorded in ScreenToGif and using other tools with converters that remove colors would result in lower file sizes. Strangely, I tried the following workaround and -- for reasons I can't explain, none if to worked. Fewer colors (black and white, 64 color, 8 color even) strangely resulted in LARGER files sizes. I really can't explain why as I've done this previously with other GIF animation tools with very different results.
Workaround:

Output
256 colors:

Black and White:

Note that converting to APNG format did nothing. The files with more colors were still somehow smaller. Maybe it's the converter I was using.
With the encoder v2.0 you can reduce the number of colors.
Wow, it was that easy? Jeeze.

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With the encoder v2.0 you can reduce the number of colors.