Are there any sources about an ancient cultic worship of one's own reflection (in water)? Have historians found any evidence of such a phenomenon?
The idea is found in some early Jewish commentaries: The Bible relates that Gideon amassed an army of 32,000 men, but God dismissed the idea of defeating the Midianites with such a large force because it would not be apparent that the victory came through Him. Instead, the army was eventually whittled down to 300 men by way of a unique litmus test: Gideon took his men to drink from a pond of water and God commanded that all those who kneeled while sipping from the water, were disqualified from Gideon’s army (Jud. 7:1–8). The classical commentators have explained that only those men who lapped with their hands to their mouth to drink water were considered righteous enough to join the army, but those who kneeled were not. Those who kneeled displayed idolatrous tendencies by revealing that they were accustomed to kneeling. R. David Kimhi explains that they either bowed to Baal or to their own reflection in the water.
The notion of people worshipping their own reflection is found in several places in rabbinic literature: The Talmud (TB Nedarim 9b) tells of an individual who became a Nazirite because he saw his reflection in the water and was inspired to commit a sin, which some commentaries explain means that he wanted to make himself into a god (see Shitta Mekubetzes there and Pirushei u-Nimmukei Rabbeinu Ezriel to TB Nazir 4b). Elsewhere, the Talmud (TB Chullin 41b) outlaws slaughtering an animal next to a pond of clear water because it looks like one is slaughtering the animal as a sacrifice to his own reflection.