I think it would be considered either horror or dark fantasy
80s or 90s, possibly early 2000s
First, it is NOT the 'Lover's Vow' from Tales From the Darkside, though it could easily have been based on the same Japanese fairytale.
It involved a man, dark haired, longer hair I think than in Lover's Vow. Forgot the intro but he finds? helps? a young woman who he gets involved with. I keep thinking of van Morrison's Moondance and that he might have been a (folk) musician/singer, but I could be wrong. She tells him that for some reason she cannot ever go out in the sun. Love. Child? He screws up and does something that causes sunlight to fall on her. She tells him to leave? turn away? I think he does not. She becomes a gargoyle and tells him she can never return. In the end he keeps looking for her, walking around calling her name , looking at/for gargoyles. I think it may have closed with a stone gargoyle shedding a tear, but as I write tales that could be my imagination. I would love to find this film again. I have no clue if it was North American or European made, but the man was dark haired Caucasian, Mediterranean, or at most mid-eastern. I would say more likely Italian or Spanish at most though.