Eyeless birdseye is a any typical birdseye maple board that has areas of wood where the curly, mottled figure is evident but without the eyes. Basically, there can be a board with birdseyes on one side, or one end, or an area in a birdseye board where there are no eyes. It's still wood from a birdseye maple log, the exact same wood but without the actual eyes. There's nothing rare or unusual about it. It's found in every birdseye log. It's just a totally different figure than can be found in any other wood or type of maple.
Turn a birdseye maple cue to where you can see the curly area on the spine, between where the birdseyes form on the face grain. It's a look that is somewhere between quilted maple & curly maple but not exactly like either. It's caused by grain growing/forming around the eyes & this causes wrinkles in the wood. As the tree grows larger & the eyes spread out like a tatoo on a skinny chick that gets fat, then there are wrinkled areas that get stretched out & have few or no eyes on it. This is eyeless birdseye. Nothing mysterious, nothing spectacular, just a sub-category of figure that can be found in maple. It's still birdseye maple, just a section cut from the log or board that doesn't display the eyes, only the wrinkles. I hope that clears things up a bit.
As for sunwood, I haven't heard of it.