Trading tips for gutting, transferring, and carving the real thing.
I use a small exacto knife for those fine details. You have to be super careful, it will slice right through, but it does amazing detail work.
I tend to really use my tools to the best of their ability. If I need to do an eye of sorts, I always have the ZP detail knife handy. Can't give much of an opinion on what drill bit to use. But what I can say is this, if you use the knife to its full potential, you can get some REALLY small cuts going.

I like to drill a hole into a section that's small enough to do so, as to give me some wiggle room (if needed of course), then use the knife to pick off the corners, thus proceeding into the piece to cut out.

Hope this helps!