For that matter, when did ghosts become translucent? In a lot of the folktales I've read (and I think also in Shakespeare iirc), ghosts look just like living people. In these cases, their true nature isn't realized until they do something to give themselves away, such as disappear suddenly. So where did we get these other images of ghosts from?
/u/rinabean has linked to my previous answer on the subject, and yes, the shrouded ghost makes its appearance in medieval texts and illustrations. As you have hinted at, however, ghosts manifest in a wide variety of shapes and forms. More often than not, the state in which the dead appeared was influence by a myriad of elements, including the cultural and theological contexts within which the author was writing and the specific rhetorical or literary point they were attempting to convey. It's a bit of a non-answer, but chasing down origins for certain literary or anthropological tropes can be a bit difficult, particularly when we consider that the meaning and value of specific symbols can --and certainly do-- change over time. While there is certainly a precedent for the shrouded phantom in the Middle Ages, the white and disappearing ghost we know and love today is more a product of the 19th century, and that is unfortunately an area with which I have little expertise. However, if you have any follow up questions, please feel free to ask!