Sorry if not using the correct language.

My best guess...

From "skeletons in the closet". Colloquially, meaning to have secrets.

Like you want the community to describe why hiding in a closet is a place to hid and a garage basement, bedroom, etc are all room of which would have a place like a closet to hide in.

Has nothjng to do with the closet to my knowledge and was always just being about hiding.

It was illegal to be a gay male in England.

Being gay required living two lives ... and one of them you had to keep in the closet. One life had to act straight and maybe even have a "beard" to appear straight.

But the other life, being gay, required some level of putting away one part of one's being for safety.

Here is a Time article about it.

In my head the closet part involves someone jumping out of bed and hiding in the nearest place to hide. A closet.

I’m almost tempted to see how far back closets became common. I’d think chests or armoires would be first.

The pre-1950s focus was on entrance into "a new world of hope and communal solidarity", whereas the post-Stonewall Riots overtone was an exit from the oppression of the closet.[15] This change in focus suggests that "coming out of the closet" is a mixed metaphor that joins "coming out" with the closet metaphor: an evolution of "skeleton in the closet" specifically referring to living a life of denial and secrecy by concealing one's sexual orientation. The closet metaphor, in turn, is extended to the forces and pressures of heterosexist society and its institutions.

https://en.wikipedia.org/wiki/Coming_out

Isn't "keeping it in the closet" an English language idiom that just means "to keep it secret"? I'd always figured "coming out of the closet" evolved from there.

Like the comment protist copied from Wikipedia, it's generally considered to be a mix of coming out with the truth, and having skeletons in the closet. Back in the eighties, that was the explanation I heard most often when hanging out with gay folks.

Doesn't necessarily mean it's absolutely factual, I'm not aware of anyone that's really dug into it with serious historical rigor. But it is at least the accepted explanation. And it makes sense, so I've never gone digging beyond talking to people alive and active during the early gay rights era of the seventies.