First, we know for a fact that the government does not have any aliens (of the extraterrestrial variety). If there were any, then Trump would have blabbed about them within the first month. He was sworn to secrecy? Since when did he ever keep a promise?
"Alien" also refers to foreigners. As a child in the 50's I watched Superman on TV and read DC comic books which regularly featured extraterrestrial aliens. Finally one day I asked my mother and she assured me that Superman and aliens were not real. OK, I could deal with that. At that time, non-citizens were required to go to the post office to get a registration card to fill out and submit at the end of every year. So there I was, knowing that aliens don't exist, watching this public service announcement reminding all
aliens that they must register with the government. "Mom!?! But you told me they don't exist!"
It has been suggested that
infrasound could be involved in ghost sightings. It seems that 19 Hz is a resonant frequency of the human eyeball, so a signal at that frequency can induce visual hallucinations. It helps if there's a room with the right dimensions to make it a resonating cavity. Infrasound can also be felt by the body triggering emotional responses such as uneasiness or dread. I'm just not sure why such visual hallucinations should manifest as a female figure.