Comment by danbruc

That is actually wrong, the equivalence principle requires careful wording. Imagine a point mass. Gravitational forces will always point directly towards it and therefore the direction of the force you measure within the elevator will vary a tiny bit in order to point exactly towards the point mass. It will also vary a tiny bit in strength because of the varying distance to the point mass depending on where you measure it within the elevator. On the other hand normal acceleration of the elevator will not show any dependence on where you measure the force.