If you are interested in just the answer and not the
rendered animation you could place the camera at
your target object location, then point it at the mirror.
Then just place something like a torus in the sky
along the path of the sun with hash marks in the texture
so you can see where the sun will pass at what time.
Place the camera at both sides of your object, you
should only have to render this twice to get the
variation in when the shadow will start passing over
the object.
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