Sam Holmquist is my “GIF Guy” and I resort to him for all things GIFs. He and I run AwkwardElevatorInc.com together and Sam is the one who makes all of our hilarious* GIFs come to life.
The arbitrary and somewhat mystical nature of Tumblr’s GIF limits have driven Sam to the brink of insanity. I just asked him for an answer to your question and his response was a mix of curse words, boops and beeps, and cat sex noises.
After putting all that into Google Translate, I got this:
The official Tumblr GIF size limit is 1MB but most things I’m able to upload around 1.25. The Breaking Bad GIF from last night was just under 2MB. The width limit is SUPPOSED to be 500px, but the Breaking Bad GIF didn’t work until I changed the width to 400px, and then I kept raising the image quality until it was just under 2MB.
Some GIFs I even have to change to 300 or even 250px. Basically, you just have to keep reducing the GIF size and width until it works.
Sam does all that in Photoshop. I don’t even know what that is. I think you buy photos in it. The Frogman has written an extensive article explaining how to use photoshop to make Tumblr friendly posts, but it was written back when the GIF size limit was 500KB.
I hope this helps.