'Oetzi the Iceman' refers to 5,300 year old mummified human remains found in the Italian Alps in 1991. A new model of Oetzi has been made for display in the museum created for him in Bolzano, Italy. Consistent with analyses of his DNA the model will depict him as having brown rather than the previously thought blue eyes. His new model coincides with the 20th anniversary of his discovery.
Genetics, eye color is a result of your DNA.
So I would presume that they have found enough DNA to find the markers that are associated with brown eyes.