Measurements of fusion cross-sections of 7Li and 12C with 198Pt at deep sub-barrier energies are reported to unravel the role of the entrance channel in the occurrence of fusion hindrance. The onset of fusion hindrance has been clearly observed in 12C + 198Pt system but not in 7Li + 198Pt system, within the measured energy range. Emergence of the hindrance, moving from lighter (6,7Li) to heavier (12C,16O) projectiles is explained employing a model that considers a gradual transition from a sudden to adiabatic regime at low energies. The model calculation reveals a weak effect of the damping of coupling to collective motion for the present systems as compared to that obtained for systems with heavier projectiles.