Quantum entanglement of K and B mesons allows for a direct experimental test of time-reversal symmetry independent of CP violation. The T symmetry can be probed by exchange of initial and final states in the reversible transitions between flavor and CP- definite states of the mesons which are only connected by the T conjugation. While such a test was successfully performed by the BaBar experiment with neutral B mesons, the KLOE-2 detector can probe T -violation in the neutral kaons system by investigating the process with K_S → π^±l^∓ν_l and K_L → 3π⁰ decays. Analysis of the latter is facilitated by a novel reconstruction method for the vertex of K_L → 3π⁰ decay which only involves neutral particles. Details of this new vertex reconstruction technique are presented as well as prospects for conducting the direct T symmetry test at the KLOE-2 experiment.