The low catalytic hydrodesulfurization (HDS) activity toward sterically hindered sulfur-containing molecules is a main industrial challenge in order to obtain ultra-low sulfur diesel. In this study we report a combined Scanning Tunneling Microscopy (STM) and Density Functional Theory (DFT) investigation of the adsorption of the sterically hindered sulfur-containing molecule 4,6-dimethyldibenzothiophene (4,6-DMDBT) onto a hydrotreating model catalyst for the Co promoted MoS2 (CoMoS) phase. The molecular adsorption occurs exclusively on the Co-promoted S-edge, most predominantly in a precursor-like diffusive physisorption referred to as delocalized ππ-mode. 4,6-DMDBT adsorption directly in a S-edge sulfur vacancy is observed exclusively in S-edge corner vacancies in an adsorption configuration reflecting a σσ-coordination. STM movies reveal dynamic conversion between the σσ-mode and an on-top ππ-adsorption providing a link between different adsorption sites and hence between the hydrogenation and direct desulfurization pathways in HDS. The low overall direct desulfurization activity of 4,6-DMDBT and related molecules is consistent with the low occurrence of S-vacancies on CoMoS S-edges predicted under HDS conditions in this study.