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The present experimental work studies the dynamics of dual-polarization optical frequency combs (OFCs) based on gain switching (GS) vertical-cavity surface-emitting laser (VCSEL) diodes under optical injection locking (OIL). This study presents two main results. First, we have obtained an overall comb formed by two orthogonally polarized sub-combs with comparable span and power. The overall comb shows enhanced optical span and flatness and high coherence between its modes. The second result is that we have been able to control the polarization state of the overall comb by tuning the polarization state of the injected light by locking the same single teeth of the comb. This produces an overall comb with single polarization that is parallel or orthogonal. These are novel findings that provide for the development of efficient and compact OFCs based on GS VCSEL sources with versatile polarization dynamics.