Headfinder: ...teach me your ways. This is so cool omg
The synchronizing is easy, at least in theory: The avatar holds the cat for 120920 miliseconds (or something like that), and the signature remains still all that time. Then, the signature holds the cat 60000 ms, and the avatar is empty during that time
When an user loads a page containing your post it should load both gifs at once, and they'll look synchronous.
But there's many ways this can go wrong: Maybe you've added an extra zero somewhere, or you didn't add all the frames ms correctly. Maybe one gif loads a bit later than the other, which would be fatal if you're aiming for something more visual and detailed than a cat fading in and out of existence.
And I just thougt of something that I'll have to test and work on:
Gifs load, and animate; and when you close the tab, they freeze where you last saw, and resume when you meet them again. For someone who meets the avatar and signature all at once all the time, it will always remain synchronous.
Probably*.
But, if only the avatar is loaded (like when you're posting) it gets to keep going, whereas the signature was frozen in place. Next time you do load both they'd be at a diferent point.
*
I'm not sure whether it frezees at a frame or at a ms. If it's the later, then all is well. If [Edit] It is the former: the cat waits a minute, winks, waits another minute and disappears, while the signature waits two full minutes. if it freezes on a frame by frame basis, the avatar might restart the after-wink wait while the signature restarts it two minutes wait, bringing a desynchronization of a full minute.
I can fix this, I've just got to add extra empty frames to the signature until both gifs have the same number of frames with the same wait on each. It will be tedious, though 
