That's great^^ Honestly my parents wouldn't know how to explain it either. They say it's a 'spirit' but they don't clarify if it is a soul trapped between two worlds, or if it is just remnants of energy/memories that someone has left behind, or anything else... And I'm glad that they are so open to it.
My family has a long history of ghost stories, but I've never been told of any experience like yours. It's interesting that when I read about stories like this, it's only in the States or in the UK.. where it gets to the point that people want to ask for help, but in my parents' country, people seem to just live with them, as if they are seen as visitors and events never get too disturbing. My parents are different in that sense.. like when it comes to this kind of topic, it doesn't quite fit in with religion. We may be very connected with the church but there are also cultural beliefs that come from the mother country..and they sort of get meshed together. Like, if I translate some of the words my parents use, I might come up with something close to "dwarf" or even "mermaid." ^^ My dad lived most of his childhood in a very remote and poor area, and he would say that many times people would just go to the Witch doctor because they couldn't afford to travel to a hospital and also the medicine --and he has a lot of stories about people being cured by odd rituals and things. Technically this is taboo at the church but my parents are pretty accepting...
I don't really have any answers myself but I am working towards it. Just to get into a little more what I wrote here
It does seem trustworthy since they are doing a lot of tests than going by superstition.
Since we're dealing with something in the non-physical, there comes a lot more variables.. and you have things to fiddle with, like subjective and objective realities which can get mixed together. And by objective, I mean the world that you share with other people. In the physical world, they are fairly separate. But like in the Rarity of Male INFJs thread some people don't believe they are so rare because there are so many of them in their own lives, but they have to look outside of themselves to really compare, if it is true.
That place you go to when you dream at night.. I don't know about you, but it is sometimes very real for me, I have the sense of smell and touch. I can eat things. And you know you're not using your physical eyes, body,etc to do that. My dreams also have symbolic content. My last dream I was visited by my sister but she was in my older brother's body when he was age 7. Looked like my brother, but I
knew it was my sister. This has meaning for me (not going to say what it is here lol)... and this is "subjective". Nobody else could understand, or use the same language
So it's good that you have two sensitives there. When one 'sees' something, then the other can confirm if they see the same thing. And there is this feedback..for proof. I have to do this a lot too when I have 'experiences'. ^^I don't want to just go for the belief.. And I think this is what's meant by 'science'... (But I don't mean to say subjective is less important..It always depends)
Anyway I'd be scared too

That shadow thing gives me the creeps. The scariest thing about my parents' friends' experiences is that sometimes when you close the door, someone comes and tries to shake the doorknob..like they are trying to get in. <_<