What program do you use for your gifs? Sadly, if new photoshop, I don't have such - but yours always come out amazing!
I’ve been using GIFBrewery for Mac, it’s only $5 in the Mac App Store.
Typically I’ll encode with 96 colors and Ordered as the dithering option. I used to fire up Photoshop, but it defaults to the exact frame rate of the video, so the files wind up pretty massive. GIFBrewery will default to 10fps (you can adjust up, I rarely take it to 15, 10 usually works well)
Animation, especially modern animation, really can compress well. Things like the new Mickey Mouse cartoons have such clean lines and solid colors that you can get away with much larger image sizes than when I do film-based GIFs.
Another trick is if you can crop the action to a taller rectangle, do it. 500x600 is a great size for Tumblr’s dashboard. I’ll usually open a file, size the height to 600px, then crop to 500x600. If the file’s coming out too large, if I resize it from that starting point it’ll keep the same aspect ratio, and still fit in the dashboard well.
Hope that helps!