The presence of the blue-eye-associated variant at the rs12913832 position (or equivalent genetic evidence for blue eye color) in Cheddar Man’s genome would be directly readable from the sequencing data, and its presence would provide relatively direct evidence for the eye color prediction. This is why the eye color component of the Cheddar Man predictions can be stated with somewhat more confidence than the skin color component, which depends on a more complex multi-gene model.
The evolutionary history of blue eye color in European populations is a topic of ongoing research. The blue-eye-associated variant at HERC2 appears to have arisen in one individual somewhere in northwestern Europe approximately 6,000 to 10,000 years ago — within the timeframe of, or slightly predating, the Mesolithic. This timing is consistent with Cheddar Man having carried the variant: it need not have spread from his exact population, but the estimated age of the mutation is broadly compatible with its presence in a person who lived 10,000 years ago.
Why the blue-eye variant spread and became common in European populations — rising from a single origin to a substantial frequency in many European populations today — is not fully understood. The selective advantage of blue eyes, if there is one, is not obvious. Vitamin D synthesis is not meaningfully affected by eye color. Hypotheses involving sexual selection have been proposed — the argument being that blue eyes are visually distinctive in a way that could confer mating advantages in a population where they are relatively rare — but these hypotheses are speculative and not definitively supported by current evidence.