The transition metal dichalcogenide 1T -TiSe2 is a quasi-two-dimensional layered material with a phase transition towards a commensurate charge density wave (CDW) at a critical temperature Tc ≈ 200K. The relationship between the origin of the CDW instability and the semimetallic or semiconducting character of the normal state, i.e., with the non-reconstructed Fermi surface topology, remains elusive. By combining angle-resolved photoemission spectroscopy (ARPES), scanning tunneling microscopy (STM), and density functional theory (DFT) calculations, we investigate 1T -TiSe2−xSx single crystals. Using STM, we first show that the long-range phase coherent CDW state is stable against S substitutions with concentrations at least up to x = 0.34. The ARPES measurements then reveal a slow but continuous decrease of the overlap between the electron and hole (e-h) bands of the semimetallic normal-state well reproduced by DFT and related to slight reductions of both the CDW order parameter and Tc. Our DFT calculations further predict a semimetal-tosemiconductor transition of the normal state at a higher critical S concentration of xc=0.9 ±0.1, that coincides with a melted CDW state in TiSeS as measured with STM. Finally, we rationalize the x-dependence of the e-h band overlap in terms of isovalent substitution-induced competing chemical pressure and charge localization effects. Our study highlights the key role of the e-h band overlap for the CDW instability.