When making GIF animations in the past, I generally use
Microsoft GIF animator.
It's pretty basic, and most of the work I do with it involves copying and pasting in paint.
Basically, you have to create each frame individually and then paste them into the program. So in order to create a bobblehead, you'd have to generate each frame of the unit individually.
Then, with the program you can edit how long each frame stays on the screen. Preview it and tweek it until you've got things the way you want. And then you're done. The only downside is, once you've saved an animated GIF, you can't go back and edit it. You would have to start from scratch.
It's a mild pain in the ass, and the results aren't all *that* impressive. But it's a fun diversion, I guess.