The idea of a ghost being formless goes back very far indeed.
If we look at Hamlet, we see that the Ghost is never said to be the revenant of Hamlet’s father (Hamlet senior, actually). It looks like it, it talks like, Hamlet wants it to be, and, as the play unfolds, it proves to be telling the truth about other things, so that we may reasonably assume that it’s telling the truth to Hamlet when it says that it’s his father’s spirit returned – but Shakespeare never claims that it is. Indeed, the guardsmen (Bernando and Francisco, IIRC) and Horatio are never willing to commit themselves further than to tell Hamlet that they’ve seen something that looks like his father’s ghost – it coiuld be any evil (or, perhaps, not-so-evil) spirit that takes that form for its own purposes. When the Ghost finally appears to Hamlet, Bernando says of it, “Looks 'a not like the King?”, not, “'Strweth, 'tis the King!”, and Horatio spends several lines trying to dissuade Hamlet from talking to it, lest it suddenly take some other horrible shape that drives him to madness, suicide, or both.
Other “ghosts”, like Dickens’ Ghosts of Christmas Past, Present, and Future, are of course not the ghosts of any particular person – “ghost” should be understood in its older meaning of “spirit” – like the Holy Ghost (in fact, I believe that I’ve seen adaptations of A Christmas Carol that call them “spirits”, not “ghosts”).
A white sheet is probably a good material representation of what a spirit was imagined to be – someone that has no inherent form of its own, but takes the appearance of whatever it deems most effective.
“Kings die, and leave their crowns to their sons. Shmuel HaKatan took all the treasures in the world, and went away.”