People have claimed they've seen ghosts, heard them, seen them move objects and so on. The evidence so far consists of claiming explicable things were ghosts: fuzzy images on film and video tape, recorded noises and static people claim contain words, cold and warm spots, and electric fields.
So to ask what would prove a ghost existed one would need to start with a viable hypothesis, and the hypotheses so far consist of totally making up things the ghosts are supposed to do or look like. Why would a cold spot be a ghost? There is no reason other than someone made up a silly explanation for temperature variation in a room. Same with the rest of the claims.
If someone existed outside their body there have been experiments designed to test this hypothesis and those experiments have not turned up valid evidence. Houdini tried to contact the dead and failed multiple times.
The bottom line is, what do you hypothesize a ghost should be able to do or what do you hypothesize you would see if you saw a ghost? This is quite a hurdle to start with since you have nothing to go on.