Cats also smell things we can't.

I say let the Cat go for it till it is satisfied; Drywall is easy to fix except for the Painting.

Maybe You have one of those Animals that will find some Valuables hidden in the Wall.

Ghost? I have seen Dogs stare of in a direction where there is nothing and have the Hair stand up on their backs. Maybe Cats are similar.

Is the Cat all or part Siamese?
My Mother had a Siamese Cat that frequently would be peacefully sleeping and suddenly jump up and run top speed through ever room in the House; and run back to the Sleeping spot and settle down as if nothing had happen. Seemed a little crazy to Me.

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84 300D, 82 Volvo 244Gl Diesel