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If I put charge on the tip of a rod and shake it back and forth at the right frequency, can I illuminate my surroundings?

According to my understanding of Maxwell equations this would create EM waves that would provided the right frequency to be be registered as light.

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    – David Z
    Commented Mar 31, 2020 at 23:23

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By shaking your wand, you would produce electromagnetic waves with the same frequency as your wand-shaking. The waves thus produced would be extremely weak ultra, ultra, ultra-low frequency radio waves which your eyes are not sensitive to.

So you would still be in the dark.

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I think the spirit of your question is "If I somehow manage to shake a charge at the right frequency, will it emit visible light?". In this case the answer is yes: this is exactly what free electron laser does. But instead of having an object holding and shaking the charge, the charge itself is passed through an alternating-polarity magnet and thus oscillates, emitting synchrotron radiation.

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