For several decades, broadband spectroscopy and fast X-ray timing have been the primary tools for investigating the rich and often intricate phenomenology of nonpulsating neutron stars in X-ray binaries with weak magnetic fields. However, available information has been insufficient to unambiguously disentangle the relative contributions of the different emitting regions, since different geometries and physical scenarios can produce similar signatures. Nowadays, X-ray polarimetry provides the missing, independent set of observables—polarization degree and angle—that are directly sensitive to understanding the nature and geometry of the emission regions. GX 13+1 is among the most peculiar systems of this class. We observed it with the Imaging X-ray Polarimetry Explorer (IXPE) over four distinct epochs, enabling the first polarization measurements during dips. A joint analysis of IXPE observations demonstrated that the polarization properties varied in response to intensity and spectral hardness changes associated with the dips, indicating the presence of multiple components contributing to the polarized X-ray emission. In particular, during dips, when the flux is lowest because the central region, hosting the spreading layer, boundary layer, and central neutron star regions, is obscured, the measured polarization can be attributed either to an extended accretion disk corona or to a disk wind component. Both of these emitting regions, if partially obscured, may explain the observed changes in the polarization angle. I will present the results of the IXPE observations, focusing on a recent observation conducted during the source's long periodic dip, which confirms that polarization tracks changes in the geometric configuration, thereby validating theoretical scenarios that have long been proposed solely on the basis of dipping phenomenology.