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That clicking noise is the key to your problems and you'll see it's coming from the compressor near the back of the refrigerator, or it's coming from the display board. If the lights are just dimming out and not cutting out completely, that is a bad compressor which is overloading sometimes. If the lights go completely out, that is a bad display control board---both issues can be intermittent and you'd need to replace the compressor or the display board to fix the issue.
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