what determines which gene is the wild type? is it just the dominant allele?

Answer 1

Officially the 'wild type' is the most prominent variation in the population. So I suppose you might call genes that produced brown eyes the 'wild type' of those genes.

Usually the term is used to distinguish between an original gene and a specfically mutated one. You'd only know that from context, but because of the contrast the 'wild type' may itself be common or not.

Most mutations tend to be recessive. So most 'wild type' genes will be dominant. This, however, is not necessarily so.