What does an unconformity in a sequence of rock layers reveal about geologic history?

An unconformity / discontinuity is a place from which some of the evidence is missing. Sills, Dikes, Faults and so on are examples.

One may infer that such and such an action has taken place, but there remains no evidence of where the fault moved the rock to.

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No! Wrong! Sorry!

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For a start the examples above are not unconformities: sills and dykes are igneous intrusions, faults are shear-fractures in which the rocks on one side of the break are moved across those on the other side. And there IS evidence when a fault is observed, of "where the fault moved the rock to". The movement is called the "Throw" and if not exposed on the surface can be found in boreholes or seismic surveys.

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An unconformity is the result of new rock being deposited on an eroded surface of older rock, with the expected intervening succession missing - either not laid in that location anyway, or it was laid down then eroded away.