In this work we study the relationship existing between the localization properties of the diluted and non-diluted direct electrical transmission lines with the overlap amplitude C-ij(omega) = 2 vertical bar(IiIj omega)-I-omega vertical bar where I-j(omega) is the amplitude of the electric current function at jth cell of the transmission line for the state with frequency omega. We distribute two values of inductances L-A and L-B, according to the generalized aperiodic Thue-Morse m-tupling sequence. We find that the behavior of C-i,j(omega) is directly related to the localization properties of the aperiodic sequences measured by the xi normalized participation number, the R-q Renyi entropies and the mu(q) moments. In addition, we generalize the scaling relationship for the overlap amplitude C-i,j(omega), i.e., <(C-i,j(omega))(2q)> = (2/N)(2q) . (C) 2016 Elsevier B.V. All rights reserved.