In modern energy networks, where operational efficiency and resilience are critical, this study introduces an in-depth analysis from a multiplex network perspective - defined as a network where multiple types of connections exist between the same set of nodes. Utilizing Belgium's electricity and gas networks, we construct a five-layer multiplex network to simulate random node shutdown scenarios. We tailored the Jaccard and Adamic-Adar link prediction algorithms by integrating the concept of exclusive neighbors, thereby enhancing prediction accuracy with such multi-layered information. Emphasizing navigability, i.e., the network's ability to maintain resilience and efficiency under random failures, we analyze the impact of different random walk strategies and strategic link additions at various stages - individual layers, two-layer combinations, and three-layer combinations - on the network's navigability. Directed networks show modest improvements with new links, partly due to trapping effects, where a random walker can become circumscribed within certain network loops, limiting reachability across the network. In contrast, the undirected networks demonstrate notable increases in navigability with new link additions. Spectral gap analysis in directed networks indicates that new link additions can aid and impede navigability, depending on their configuration. This study deepens our understanding of multiplex energy network navigability and highlights the importance of strategic link additions influenced by random walk strategies in these networks.