If we disregard the human element (hallucination, poor eyesight, sincere mistakes, mental aberration, the fact of consciousness etc etc) and also arguably possible factors like environmental causes and so on, then what is left to explain the (apparent) existence of ghosts? A return from death is scientifically impossible, as far as I know; alternative dimensions of time unproven; so what remains? And why - frustratingly - if we leave aside the possible elements and causes mentioned previously, does there seem to be no single explanation?
This is clearly a sincere post, but you almost slip into what I call the "Von Daniken technique" as used by various writers on the weird and wonderful from around the time of Von Daniken's books. "If you exclude A, B, C,...,Y (see how fair I'm being!) that still leaves Z unexplained."
The next step is to say, "And if we accept that Z is unexplained, then maybe some of A-Y shouldn't have been so easily dismissed."
Your question presupposes that there are some ghosts that cannot be explained. That is not the same as "have not yet been explained". It also doesn't take into account that in many cases, there is so little data and so much inconsistency that an explanation is impossible.
For comparison, if I tell you I was in pain on Wednesday, you cannot offer a credible diagnosis of the cause. This is not because the pain is "inexplicable" but because I have given you insufficient data for any one explanation (Migraine? Broken leg? Gastroenteritis? bee sting?) to be justifiable.
You use the expression, "scientifically impossible." This is a strong term. Something is only "scientifically impossible" when it cannot possibly happen without conflicting with well established and tested scientific theories.
A man-made perpetual motion machine is "scientifically impossible" because there is extensive scientific knowledge about conservation of energy, and efficiency losses through friction and other causes.
A ghost is not yet "scientifically impossible" because science has not strayed far into those areas that
might possibly explain ghost sightings. At best, we can only say "unexplained by science".
You also show a strong preconception when you refer to the apparent absence of a single explanation as "frustrating". There is no reason why so many varied reports should fit a single explanation or theory.
To look into ghosts in any sort of rational way, we would first need some working definitions, and an agreed body of data. What we actually have is a huge amount of anecdotes (some sincere, some not), perception, folklore, misreporting (honest or otherwise), and a welter of speculative explanations, some of which are dignified with the name "theory". (The "stone tape theory" is not a theory, or even yet a hypothesis, in the usual sense of these words. At best it is a speculative explanation based on an analogy.)
What we do know is that ghosts of one kind or another have been prominent in all or most cultures in history. Apparently sincere people with good reputations have reported seeing things that they interpreted as ghosts. However, it is hard to separate these "credible" reports from all the folklore, the FOAF accounts, and the "They do say..." stories.
As others have remarked above, this may be more of an area for the philosopher (and the psychologist?) than the scientist. This may never change. Scientists need reliable data, testable hypotheses, and repeatable experiments, and it is unlikely that ghost research will ever offer even the first of these, never mind the last.
Many explanations for ghosts involve the spirit or soul of a deceased person remaining active after the body has died. We do not yet have an accepted explanation or formal definition of a spirit or a soul. It is a remarkably challenging problem for philosophers. If consciousness is an emergent property of brain activity,
who is conscious of it? If self-awareness is an emergent property of brain activity,
who is being aware? If the spirit is separate from the body, but inhabits it, what "powers" the spirit? What binds it to the body? How does the immaterial spirit experience the physical senses (touch, sight, hearing, etc.) of the body? If the spirit needs the body in order to exist, then how could it survive after the death of the body? If it does not need the body in order to exist, why is the spirit so closely associated with the body?
I think some of these things are inherently unknowable. Not everything can be explained, and not everything that can be explained can be tested.
Personally, I think it is overwhelmingly likely that all ghost reports arise from circumstances that could be rationally explained with our current level of knowledge if only we had sufficient data. Trouble is, we never will: if I see a hooded figure in the distance, there are so many variables that could come into play before I can record it and report it and you can investigate it.
If I see a small bird fly past me into a hedge row, then it flies away on the other side of the hedge before I can identify it, there has clearly been an event explicable with our current level of knowledge (it may have been a sparrow, or a wren, or a finch, etc. as they are all common near where I live) but it will never be wholly explicable because my honest report will lack detail, and the evidence is not longer there. It may simply have been a female house sparrow, but we will never
know.