Mindfulness one of the key skills(if not THE key skill) exercised by meditation is the ability to be aware of one's own thoughts and feelings, and this is practiced primarily by listening to what thought's were having, and letting them go.
I never fall into a deep sleep. Sometimes I trance out into heady thoughts where the outside world gets blocked off.
I don't really know where meditation ends, naps begin, and where legit sleep falls in the spectrum. My goal isn't meditation though, my real goal is to black out cold, but haven't gotten there yet. So ymmv for anyone else attempting but it seems I'm in the same field as you describe.
Then I tend to naturally snap out of it before my alarm rings me awake.
Tools: travelers sleep eye mask, comfortable silent area (my car in parking garage), phone timer.
The same way we are aware of moving our arm when we are doing so, becoming aware of your thoughts while we are thinking. We tend to take are thoughts for granted, giving them automatic truth status
I prefer to just become an observer of my thoughts; to acknowledge and let them flow; I focus on accepting that they are only thoughts - little impulses. The imagery I often have is that I'm sitting in a clear bubble, and my thoughts are swirling around me: I can see them, and I know they're there, but I do not let them in.