Giant Random Telegraph Noise (RTN) in the resistance fluctuation of a macroscopic film of perovskite-type manganese oxide La2/3Ca1/3MnO3 has been observed at various temperatures ranging from 4K to 170K, well below the Curie temperature (TC = 210K). The amplitudes of the two-level-fluctuations (TLF) vary from 0.01% to 0.2%. We use a statistical analysis of the life-times of the TLF to gain insight into the microscopic electronic and magnetic state of this manganite. At low temperature (below 30K) The TLF is well described by a thermally activated two-level model. An estimate of the energy difference between the two states is inferred. At higher temperature (between 60K and 170K) we observed critical effects of the temperature on the life-times of the TLF. We discuss this peculiar temperature dependence in terms of a sharp change in the free energy functional of the fluctuators. We attribute the origin of the RTN to be a dynamic mixed-phase percolative conduction process, where manganese clusters switch back and forth between two phases that differ in their conductivity and magnetization.