Movies like Eye of the Beholder

British Consulate investigator Det. Stephen Wilson, a.k.a. the Eye, comes across a disturbed lady serial-killer while on an otherwise mundane assignment. Already a bit psychologically fragile from his wife's abrupt removal of herself and their daughter from his life (with the lingering memory of his daughter haunting him like a manifest ghost), his psychosis as a displaced dad dovetails with the femme fatale's psychosis as an abandoned daughter (crying "Merry Christmas, Daddy" over her expired victims). A bond forms, or, rather, an obsession, as the Eye abandons his job to secretively stalk this mysterious woman full-time as she visits many major U.S. cities under various names, leaving numerous victims.