Unfortunately for you I'm more afraid of disappointing my wife than I am of disappointing you. If I took that lamp apart and broke or lost something, well, let's just say "It would be bad" to quote the Ghostbusters. 
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Is the base shell ferrous metal? If not, see if a magnet is attracted to the “evil area”.
Try running a magnet around underneath.
Good idea, but it's 100% ferrous...magnet grabs it everywhere...
Also looked on the bottom and there isn't any screw(s) to access the interior, looks like it just glued together. So that's not happening.
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I was kind of thinking maybe where the cord comes in it has some sort of strain relief loop inside the base. That could create a tiny magnetic field. Maybe it is only looped on the one side where there is a problem.
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Definitely a Nortul Capacitor.
So you are going to disassemble the base then?. It's better to disappoint your wife than us bunch here I am sure.
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Apologies to everyone, but the relationship math is not on your side. 
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CT Scan?
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You wouldn't have this problem with a dashboard.... 
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