I found my old Intuos 4 3 mouse zc-100-02 (this model https://www.amazon.com/Wacom-Intuos3-Five-button-Mouse-mouse/dp/B0006698TW)

And tried it with my two Wacom Intuos Pro Large PTH-860 tablets. Neither tablet reacted to it at all. The Wacom driver didn't even recognize the mouse existed.

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EDIT: I had originally mistakenly written that this was an Intuos 4 mouse. It is actually the Intuos 3 mouse.