A variation of the Millikan Oil-drop experiment could be used to directly measure electric fields around a rotating magnet. Consider a disk magnet polarized through the plane of the disk, the top face north, bottom face south. The magnet is placed in a horizontal plane and spun about a vertical axis through its center. If the magnetic field turns with the magnet, one might expect a v cross B electric field to be produced above it. Near the magnet surface this would appear as lines running parallel to the magnet surface, radiating from the axis. (The resulting field would look very much like some charge had mysteriously appeared in the space above the magnet.)
To measure any fields, drop very small charged oil droplets above the magnet and watch their paths as they fall toward it. Any electric fields should deflect the droplets. The droplets would need to be shielded from any air currents produced by the spinning magnet.