In this work, we report measurements of viscosity and density near the liquid–liquid phase transition of the binary solution of the room temperature ionic liquid (RTIL) 1-methyl-3-hexylimidazolium tetrafluoroborate (C₆mim⁺BF₄⁻) in 1-pentanol. The density and the shear viscosity have been determined as function of the temperature and of the concentration. The critical point is located at the temperature T_c = 314.91 K and the mass fraction w_c = 0.31034 of the salt. For the critical concentration, the viscosity measurements yield an enhancement as expected for Ising criticality with a crossover to regular behaviour. The regular background is obtained by interpolation from the measurements at non-critical concentrations. The critical enhancement is well described by the mode-coupling crossover function of Bhattacharjee et al. (Phys. Rev. A, 1981, 24, 1469) .The closed form result of the limiting case q_D/q_c → 0 matches the data almost perfectly.