We present a high-pressure investigation of the semiconductor-to-metal transition in MoS2 and WS2 carried out by synchrotron-based far-infrared spectroscopy, to reconcile the controversial estimates of the metallization pressure found in the literature and gain new insight into the mechanisms ruling this electronic transition. Two spectral descriptors are found indicative of the onset of metallicity and of the origin of the free carriers in the metallic state: the absorbance spectral weight, whose abrupt increase defines the metallization pressure threshold, and the asymmetric line shape of the E1u peak, whose pressure evolution, interpreted within the Fano model, suggests the electrons in the metallic state originate from n-type doping levels. Combining our results with those reported in the literature, we hypothesize a two-step mechanism is at work in the metallization process, in which the pressure-induced hybridization between doping and conduction band states drives an early metallic behavior, while the band gap closes at higher pressures.