  A key feature of topological insulators (TI) is symplectic symmetry of the
Hamiltonian which changes to unitary when time reversal symmetry is lifted and
the topological phase transition occurs. However, such a crossover has never
been explicitly observed, by directly probing the symmetry class of the
Hamiltonian. In this report, we have probed the symmetry class of topological
insulators by measuring the mesoscopic conductance fluctuations in the TI
Bi$_{1.6}$Sb$_{0:4}$Te$_2$Se, which shows an exact factor of two reduction on
application of a magnetic field due to crossover from symplectic to unitary
symmetry classes. The reduction provides an unambiguous proof that the
fluctuations arise from the universal conductance fluctuations (UCF), due to
quantum interference and persists from T = 22 mK to 4.2 K. We have also
compared the phase breaking length (l$_\phi$) extracted from both
magneto-conductivity and UCF which agree well within a factor of two 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.
