There are indeed a few Grey Cock variants with a ghost in them; as I said, the revenant verses are borrowed from other songs. Consider it as a night-visiting song which occasionally has supernatural elements; though these are not native to it.

For a detailed analysis, see Hugh Shields, 'The Grey Cock: Dawn Song or Revenant Ballad?' in E B Lyle, Ballad Studies, 1976. I found his arguments convincing, though my own, far more limited, examination of variants had pre-disposed me to that opinion. Anyway, Shields is a real authority (unlike me) so you'll have to disagree with him as well!