Your claim is that there is some critereon by which the entire population can be sorted into either female or male with no third category. For some reason, you are not able to identify what this critereon is.

No, you're not feigning ignorance about the peafowl. A male phenotype can have either a male or female genotype. What are you trying to prove?

So which determines sex -- what something looks like, what its genes are, or neither?