According to a recent study, Neanderthals had already died out before those blue/green eye colorings appeared in the evolutionary tree.
https://www.positivemed.com/2013/12/08/surprising-origin-blue-eyes/
Yup. The blue eye mutation is reported to have occurred only once.
Everyone related to me has our characteristic bright blue eyes.
9,000 year old Cheddar Man had blue eyes. He has the same DNA (U5a) as my dad's mother, grandma Smith. He is also reported to have had dark skin too. My employees used to tell me that I resembled Paul Newman.