Electromagnetic Time Reversal (EMTR) features the bounded phase property, a well-established and reliable method for fault location in two-conductor transmission lines. Under the EMTR-based framework for mismatched media, this property asserts that the phase of the overall forward and backward transfer function remains strictly confined at the true fault location. Extending this property to multi-conductor lines is challenging because the transfer function ceases to be a scalar and instead becomes a matrix. Nonetheless, in this paper, we demonstrate that the bounded phase property applies to all eigenvalues of the transfer-function matrix, thereby providing a clear pathway for its application to multi-conductor lines.