Remember something, detecting something invisible (or heavily obscured, which is what invisibility is) doesn't tell you the exact location. It tells you where that thing is in a 5 foot square. It tells you that something is at that location and enough of a something that I can tell something is there, even if I don't know exactly what.
So, yeah, your pane of glass in the rain is enough for someone to know that there is something there. They can potentially see that there is something odd about that location. They'd still have disadvantage to attack that location and couldn't target it with anything that requires you to see the target, like Hold Person, but, they'd still know enough to be able to shoot arrows in the right neighborhood.
The invisible gargoyle is the same thing. It rushed into the room. Maybe there is dust on the floor, maybe there is dust in the air that's disturbed by its passage. Maybe the rogue managed to open the door before the gargoyle completely managed to stop moving. Maybe it's a wooden floor and the half ton gargoyle is making some dents in the wood leading to where it stopped. Whatever. That's what passive perception is for.
Now, if the gargoyle had actually taken the Hide action? Now he's Hidden until the PC's take an action to find him.
Maybe our flying wizard sparkles a bit from the Fly spell. Maybe he's not as quiet as he thinks he is. Maybe a flash of lightning causes the invisibility to ripple a bit. Whatever. Again, until he actually takes a Hide action, he isn't Hidden.
AFAIC, that's the bottom line. Hidden is a condition in the game. It is not the same as the plain English word hide. Hidden is a condition that requires a Stealth check. Other than something like Etherealness or a few other exceptions, you cannot apply the Hidden condition without one.
Heavily Obscured, again, another game defined condition, is not the same as Hidden. Heavily Obscured is a lot easier to achieve. Standing in a dark room satisfies that. But, Hidden, as a condition, requires a Hide action. At least, that's how I rule. Otherwise, invisibility becomes far, far too powerful.
I mean, why does my rogue ever have to make a Stealth check? I'm in an area that is Heavily Obscured, so, I am automatically Hidden so long as I don't move? I want to play a Shadow Path Monk in that case. Wahoo, I can teleport every round and I'm automatically hidden each time, so long as I stay in shadowy areas? Go go ultimate ninja.
This is why I don't like your interpretation. It has far too many knock on effects and causes all sorts of corner case issues where the player constantly has to refer back to the DM to determine his or her actions. No thanks. I think I'll go with a simple solution that applies virtually universally. Reduces frustration, makes the game run faster and smoother and removes all the arguments. Yup, that's the way I roll.
