Well, that’s interesting. If I were presented with incontrovertable evidence that ghosts existed, it would be very interesting. But it would depend on what sort of thing ghosts were.
Are they some sort of “recording”? Or are they some extra-material component of human consciousness that somehow can be separated from the material part? Or maybe they are really aliens, or holograms, or something we don’t understand.
It all comes down to, are these proven ghosts actually proof of life after death? Are they proof of life after death for everyone, or just the ones that become ghosts?
If the ghost prove that there is some sort of extra-material component to human consciousness, what relation does it have to the brain? What sort of stuff is it? If ghosts exist, they will be amenable to scientific investigation.
But, there mere existance of an extra-material component to human consciousness does not prove that God exists, or that the said component has some sort of existance after death. Perhaps the “soul” is completely natural, and is an expression of hitherto unknown natural laws. Maybe other things have “souls” too…animals, plants, rocks, planets. Perhaps there are “souls” that have no association with normal matter…spirits, angels, or demons. And perhaps such non-material entities had some relation to the beginning of life on earth, or the formation of the universe.
But that would be a matter for scientific investigation, not an uncritical leap of faith.