Sankara consistently uses arguments which are on the weak side not because he hasn’t got others. They act as placeholders for the inquiry. He has placed his staff upon the area that he wishes the aspirant to knowledge to focus on or to work through. This is like the method of the vedanta according to Swami Satchidanandendra – false attribution followed by retraction. Arguments seemed to be graded according to the ability of the student to process them. After all as he has said in the Brahma Sutra Bhasya (II.i.11) when he impugns logic and epideictic reason as a way to realisation; no matter how clever your argument someone will come up with a refutation.
Brhadaranyaka Upanisad IV.iii.6:
You said, 'Some light which is of the same class as the body and organs must be inferred, since the sun and the like are of the same class as the things they help. This wrong, for there is no hard and fast rule about this help.’
Therefore, when something is helped by another, there is no restriction about their being of the same class or of different classes. Sometimes men . are helped by men, their own species, and sometimes by animals, plants, etc., which are of different species. Therefore the reason you adduced for your contention, that the body and organs are helped by lights that are of the same class as they, like the sun etc., falls to the ground
That seems to deny the idea of causal closure suggested by the expression that the Self is in the midst of the organs, interacting with them so to speak.
Janaka in Brhadaranyaka Upanisad IV.iii.7:
J anaka cannot decide whether the self is just one of the organs or something different, and therefore asks: Which is the self!' The misconception is quite natural, for the logic involved is too subtle to grasp easily. Or, although the self has been proved to be other than the body, yet all the organs appear to be intelligent, since the self is not perceived as distinct from them ; so I ask you: Which is the self?
The solution is developed in a long commentary on that sutra which also deals with Buddhist objections.