This is what is under the cover you see when you look at your windshield wiper.
It is the reciprocal mechanism which makes the wiper arm go up and down.

The arm (labeled on the left) is rotated about the arm rotation point indicated on the right (it is also the back side of the small gear in the previous picture). This causes the mechanism circled in green (down on left, and up on right) to travel up and down the guides.
Grease the guides, but I suspect the most important spot to grease is the point where the shaft exits the housing. (labled 'grease here')

A pretty simple job with a couple of pictures. My replacement should be here by Friday.

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