Ive been around this rope/snake area before and though it looks to be quite simple it has its complications due to the fact that it is an analogical vade mecum with subtle differences in its deployment. My latest attempt to grasp its usage I offer for your metaphysical delectation.
It breaks in two, obviously, the snake and the rope or the superimposition and the substratum. The latter is the reality, in theatrical terms the back cloth upon which the ‘snake’ is painted. In Sankara’s commentary on the Mandukya Upanisad he describes it thus.
“No, for an unreal illusion cannot exist without a substratum; for the illusion of silver, snake, human being, mirage, etc., cannot be imagined to exist apart from the (corresponding) substrata of the mother of pearl, rope, stump of a tree, desert, etc.”
There enumerated are the standard examples of confusion. In a footnote Swami Gambhirananda writes:
“Since an illusion is perceived as soaked in the idea of existence, it cannot have non-existence as its basis.”
The analogy moves into the metaphysical when it is stated that similarly this mundane reality is as it were painted on the back drop of pure being. As limited contingent being it requires absolute being as its reality.
An analogy is used to express what is beyond human reality:
“For a relation between the real and the unreal does not lend itself to verbal representation, since the relation itself is, unsubstantial.”
That is then the well known general use of the confusion/delusion analogy. However in the Preamble to the Brahma Sutra Bhyasa Sankara introduces a subtle variation. Superimposition now becomes an epistomological/ontological method of transferring the really out there, in the ‘external’ world, object into the mind of the subject. That is possible because the substratum of the consciousness of the subject and that of the object is the same. This is the core of the non-dual/Advaitic philosophy. What we have is a non-numerical identity between the subject’s reality and the object’s. This is the basis of perception what in the the Vedanta Paribhasa of Adhvarindra is called perceptuality.
For the mind of the sage there is no other:
“On the view, however, that like the rope, imagined variously as the snake etc., the Self, too, though one, is imagined in the three states (waking, dreaming, deep sleep) to be possessed of such attributes as consciousness of the internal world etc., there follows the cessation of the phenomenal world of misery simultaneously with the valid knowledge , arising from the negation of such attributes as being conscious of the internal world; and therefore there remains no need to search for any other means of knowledge or any other discipline (like constant thinking/Manana?) for the realisation of Turiya/Enlightenment. This is similar to what happens in the case of the knowledge of the rope where the elimination of the snake from the rope occurs simultaneously with the discrimination between the rope and the snake.” (Sankara's commentary)