Full disclosure: I am, of course, very curious about this, but it's also for a gift for my wife. She's a historian and I've printed her a nearly-original-size Gayer-Anderson Cat. The artifact is unpainted bronze with no remaining paint. However, the Wikipedia page suggests it was originally painted.
I've searched online to see if anyone has re-created some plausible version of the original artist's coloring, but haven't found anything, yet. The British Museum's online gift shop offers this miniature but comparing to the few notes about paint on Wikipedia it's already probably not very accurate.
I'm guessing she would have had gems or glass of some kind in her eyes, earrings and a septum ring (as the British Museum has in the G-A cat), and probably all her necklaces would have been painted. Are there "standard" ways of doing the statue's eyes? And "standard" ways of painting the necklaces? I think I see an Eye of Horus and maybe a Ra (and Eye of Ra?), going only from my Wikipedia-surfing about Egyptian mythology (I'm not anything like a historian), but I don't know how those might have originally looked.
As for the statue itself, what color(s) might it have been? Wikipedia suggests the tail might have been striped (!). Would the cat have been painted to look like a common housecat or feral cat of 600BC?
Any plausible explanations appreciated. Also, any mythological background is more than welcome. I have thoroughly enjoyed reading about the myth of Osiris and other ancient Egyptian stuff as tangents arising from this project.
Edit: added link to print in its current "primer and epoxy putty" phase.
##The case for a painted cat:
The Ancient Egyptians painted most everything else: tomb reliefs, sarcophagi, themselves. It stands to reason that they would have painted statues as well, though I'm not aware of any direct evidence of this. Thousands of years in the desert sun will burn off every trace paint.
However, the statue isn't really "Ancient Egyptian," it's classical Egyptian, meaning it's from a period where either the Assyrians or the Greeks ruled Egypt. However, Greeks also liked painting their public art, so that probably onl makes the case stronger.
##The case against a painted cat:
When you see something like this (which isn't actually bronze, but gold), you might think "hey, that sure looks painted," but it's really not. It's inlaid with gemstones and glass. Look closely and you'll see places where the inlay popped out.
Bronze (and gold) is really difficult to paint and requires a lot of chemistry and/or heat. This is mostly from personal experience (I've done some statue work), but I'm also unaware of a single painted bronze artifact from the ancient world. Not from Europe, Africa or Asia. Even modern bronze statues have a muted and limited palate.
I want to disclaim that this isn't based on any massive amount of research though. If someone can prove me wrong, I would be delighted.
##About the eyes
You're probably right that the cat's eyes were inset with something, though I don't know if jewels would necessarily have appealed to the Egyptian aesthetic. Good old Sheikh el-Beled has eyes made out of copper and rock crystal. Egyptians often wanted a thing to look like it did in real life, at least in a general way. So did the Greeks.