High Refractive Index (HRI) dielectric particles smaller than the wavelength, isolated or forming a designed ensemble are ideal candidates as new multifunctional elements for building optical devices. Their directionality effects are traditionally analyzed through forward and backward measurements, even if these directions are not suitable for practical purposes. Here we present unambiguous experimental evidence in the microwave range that, for a dimer of HRI spherical particles, a perfect switching effect (perfect means off = null intensity) is observed out of those directions as a consequence of the mutual particle electric/magnetic interaction. The binary state depends on the excitation polarization (polarization switching). Its analysis is performed through the linear polarization degree of scattered radiation at a detection direction perpendicular to the incident direction: the beam-splitter configuration. The scaling property of Maxwell equations allows generalizing our results to other frequency range and dimension scales, for instance, the visible and the nanometric scale.