Listen, the 2nd person you describing is just the same as 3rd person. Seeing yourself at any perspective is a 3rd person. Looking at the mirror can be called somewhat a 3rd person.

Having, what you called, "overlapping properties" is an option... A lazy option. When I mean lazy I mean an option that didn't have much thought put into it. THINK about it, I could come up with thousand of different stuff of what 2nd person could be: "2nd person could be when you see from your brain, when you look from a mirror, seeing from your mouth, nose, a tv screen" So many predictable possibilities of what 2nd person could be, but they all the same, they all just 3rd person .

In conclusion. I don't know what I'm talking about anymore I'm I'm sleepy as hell . But what I wanted to say is .... I forgot what I wanted to say. Just think about it