If the gear or wheel is moving at a known rate, it can define the minimum speed of light passing through it, if the gear goes sufficiently fast and is sufficiently large with a sufficiently small hole.
Einstein was not infallible or all-knowing. His insistence on having two clocks when all that is needed is one time-accurate gear just shows he wasn’t thinking clearly. Einstein was clearly not an idiot.
However the mock physicist ignoring the very solution he presented is an idiot.