A key feature of topological insulators (TIs) is symplectic symmetry of the Hamiltonian which changes to unitary when time-reversal symmetry is lifted and a topological phase transition occurs. However, such a crossover has yet to be explicitly observed by directly probing the symmetry class of the Hamiltonian. In this Rapid Communication, we have probed the symmetry class of topological insulators by measuring the mesoscopic conductance fluctuations in the TI Bi1.6Sb0.4Te2Se, which shows an exact factor of 2 reduction on application of a magnetic field due to a crossover from symplectic to unitary symmetry classes. The reduction provides an unambiguous proof that the fluctuations arise from the universal conductance fluctuations (UCFs), due to quantum interference, and persists from T∼22mK to 4.2K. We have also compared the phase breaking length lφ extracted from both magnetoconductance and UCFs which agree well within a factor of 2 in the entire temperature and gate voltage range. Our experiment confirms UCF as the major source of fluctuations in mesoscopic disordered topological insulators, and the intrinsic preservation of time-reversal symmetry in these systems.