A liquid-liquid transition (LLT) is a first-order transition separating two liquid phases of the same single-component substance with different densities. Despite the long-standing and wide interest in this phenomenon, it remains poorly understood and unambiguous experimental realizations are scarce. The present proposers reported in 2020 the experimental discovery of a LLT in compressed liquid sulphur in the range 0-2.15 GPa, 450-1040 K [1]. Moreover, we conveyed evidence for a critical point ending the LLT line, long-sought in the case of water and never observed in any other system so far. The present proposal aims at better understanding the driving mechanisms and order parameter of the LLT in sulfur by measuring the shear viscosities of the low-density and high-density liquids from 0.2 to 2.5 GPa, using the falling sphere technique in the Paris-Edinburg press.