Einstein's equivalence principle and acceleration due to rotation

Einstein's equivalence principle is often illustrated by pointing out that a person trapped in an elevator has no way of telling whether they are on the surface of the earth or in deep space in a rocket ship accelerating at 9.8 m/s2.
A third alternative is that the elevator is at the end of a very large centrifuge arm with $$\omega$$2r = 9.8 m/s2. But this case could be settled easily by setting up a gyroscope and watching to see if its axis rotates. Unfortunately, there is no gyroscope available. But there is a very sensitive gravimeter available.
The question is: how does a person determine just from gravimetric measurements whether or not they are in a centrifuge and which way the centrifuge is rotating? It's easy to say that it must come from the curl of the field, but it eludes me as to exactly what set of measurements to take or why the measurements would show non-zero curl.
There is a related post here but it doesn't offer the insight I was hoping for.