Are you dipping it in the cup or a fluid bed?
After you swish it in the paint put it back over your heat source to smooth the finish out. While it's still hot take a piece of wire and run it through the eye slowly, the paint will stretch out as you run the wire through, don't pull the wire back yet, let the paint dry a few seconds then pluck it off the end of your wire and then pull your wire back out and reheat to smooth the finish around the eye.
That sounds much more complicated than it really is. I use a hook (cut off at the bend) for my wire. Some colors are are more prone to clogging the eye than others.
*not responsible for burnt fingers, you'll learn how long to wait quickly