I couldn't get a handle on the narrator's feeling about the eyes. He doesn't seem very affected by the story and just reflects on it like talking about an old relationship. It's the content itself that is creepy, but the way it's told is not.
I also noticed there were many passages that placed science and spirit against one another. I'm not sure if this is a comment about the scientific community advancing and exercising old mysticism or spiritualism, but I noticed it many times.
p. 197 "...asking my doctor for a prescription, or my occultist for a pair of spectacles."
p. 201 "I now applied myself to explaining them (the eyes) on scientific principles."
I haven't pieced it together yet, but the phrase "to justify myself in my own eyes rather than hers;" seems like a lynchpin to the story.
Is this saying that the eyes were an internal projection of his interpretation of her vision? Not sure. Interesting though.
On a side note,
I went to the James J. Hill house for the Victorian Ghost Stories event. It was pretty neat. They read (abridged) ten stories or so. They did Edith Wharton's The Lady's Maid Bell. It was tied up in a nice little production and much less ambiguous compared to the text. Go check it out if it's still going on.