I tried Firefox 3.6 out of curiosity, and it doesn't blink, even when I open the favicon itself in a browser tab. I think you must have changed your browser config at some point and forgotten about it.
In my local version of firefox, the entire icon vanishes for about 5 seconds, every 5 seconds. Causing a notable visual disturbance. In Chrome on another system the eyes blink every 5 seconds or so. So yeah, my browser is being broken.
But when I asked people if it blinked ... they, of course, said yes.
EDIT: Also, as noted in an edit above, when viewed in Chrome it didn't animate unless the image was accessed directly. So for you it may blink, not blink, or really blink, depending on your browser and configuration...