How many scientific observations of Manguedon have been made?

None - because Manguedon isn't a scientific phenomenon. Nor is it a gender. It's a cultural phenomenon in Myanmar, which explains transwomen in terms of possession of a spirit (nat), of which Manguedon is an example.

It's a very close analog to the way that many societies will adopt cultural explanations for schizophrenia - whether demonic possession (in early Europe), having contact with spirits of deceased family members (India), or speaking directly to G-d (many cultures, including Ghana). In fact, the cultural milieu in which schizophrenia manifests can affect the types of auditory hallucinations that schizophrenics report:

news.stanford.edu - Voices culture luhrmann

But the fact that a society has a clearly non-scientific explanation for schizophrenia doesn't mean that schizophrenia doesn't exist. Or that there aren't scientific observations of schizophrenia in those societies specifically. It just means that the local culture has come up with a non-scientific explanation of that condition. It doesn't make the condition any less real.

Many of the terms on that list of "genders" you have been implicitly mocking fall into the same category. They're just different cultural explanations or descriptions of gender dysphoria that have been adopted colloquially in various cultures. If a local culture has a non-scientific story surrounding a scientific phenomenon - whether it's believing that witchcraft or demonic possession is responsible for epilepsy, or that animist spirits are responsible for natural events - that doesn't invalidate the scientific basis of epilepsy or lightning. It just means they have a local myth or story to explain it.