This is a classic symptom of heat resistance corrosion in the fuse box terminals. Did the fuse box show any signs of distortion or melting at that location? At the very least you should pull all your fuses and abrade them with fine sandpaper. This holds true for the fusebox terminals too. Its a little tougher to find something to stick in them though. Nowadays it is highly recommended that the fuse box be replaced. The the new terminal are much better than the originals.
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