A couple of tips from my little bit of experience on the subject.
I keep a safety pin on the magnet of my tying station to knock the paint out of the eyes before it dries. I also keep a straight pin there for the same reason. Sometimes I will have to use both of them depending on how hard the paint has gotten.
I also use a pair of manicure scissors. I will poke the pointed tip in the eye and then rotate the scissors to finish cleaning out the area.
One last thing, I keep a large cork from what I would guess is from a magnum of wine in my tying station. If I am only doing a few heads, I will stick the jig or fly to the cork until is ready to go into the toaster oven.
Hope this helps,
Bobo