It is still difficult to point to a stream of consciousness any time that consciousness is a point discrete moment which arise in contact with its object. Eye-consciousness is a discrete moment as mind-consciousness is. Once the object is absent and contact fades, consciousness ceases. It can't continue in a way of a stream. Mindfulness, meditation discovers that discrete and point aspect of a moment of consciousness with out leaving an stream. IMO, clinging and craving leads to the idea of a stream that sound like something everlasting, when it is not.