Analyze the following argument: 'If consciousness is entirely a product of brain activity, then destroying the brain would necessarily eliminate consciousness. However, numerous documented cases of near-death experiences suggest consciousness can continue despite minimal brain activity. Therefore, consciousness cannot be entirely a product of brain activity.' Provide a thorough analysis that includes: 1) Identification of the argument's formal structure (including premises, conclusion, and logical form); 2) Evaluation of the argument's validity (whether the conclusion follows logically from the premises); 3) Assessment of the soundness of each premise (including whether they are factually true and what evidence supports or contradicts them); 4) Identification of any fallacies or weak points in the reasoning; and 5) A reconstruction of how the argument could be strengthened or, if fundamentally flawed, a counter-argument addressing the core issue. Your analysis should demonstrate advanced logical reasoning skills while remaining fair to the original position.