The Historical Jesus

[Ferrocyanide]

Because if it isn't the brain that determines this, then we are left with what?

I don't know. This seems to me a problem.

If there is no identifiable anatomical structure, or interaction (say, a balance of hormones) that determines gender, then we have no objective, testable, empirical method of determining it. 

I mean, personally, it's OK with me if people want to identify however they want. But a personal claim is not one that science can deal with.

Put in another way, we could think about falsifiability. (Remember that it's common to say that any scientific claim must be falsifiable, and if it's not falsifiable it's not science.) 

If a person claims they are one gender or another, or none, how can this be falsified? If a person says "I'm female," is it EVER possible to say "no, you're not." If not, then we're dealing with some kind of truth which is not empirical, testable, scientific. We are to believe it based on an individual's claim -- not on evidence.

Yes, it is part of the scientific method to develop a falsifiable hypothesis.

The problem in this case has to do with complexity and the limitations of science.
Problem 1: There is no way to map out the brain at the neural level and to also not damage it.
Problem 2: If some technology is invented to solve Problem 1, there is another large barrier, which is problem 2. How do we identify what a circuit does?

In electronics, it is possible to look at different CPU circuits, different calculator circuits and be able to identify and adder circuit. There are small variation in adder circuits but basically, everyone now uses the same optimized circuit.
Can the same be done for the brain? Is it possible to recognize which part store a memory about a guy celebrating his 20 th birthday?
It is possible to recognize the circuit which makes a person prefer the blue color?

Right now, we don’t have a clue. The method used is to damage the neural circuit to figure out what it was for.
This is not something that can be done intentionally on a human.

Other things are much easier to test:
What is the glucose concentration in someone’s blood?
What is the sodium concentration in someone’s brain?
Is the heart structure healthy (Use a echography to image the heart)?
Is someone’s intestines ok? (give him some barium sulfate and use a x-ray video machine to visualize inside him)