What further complicates this is the contributions of dipoles. These are the regions that are strongly anti-correlated to begin with. If the sign is maintained, then this may also decrease the average link strength during an El Nino event
A significant amount of climate research is dedicated to searching for these dipoles:
J. Kawale, S. Liess, A. Kumar, M. Steinbach, A. R. Ganguly, N. F. Samatova, F. H. Semazzi, P. K. Snyder, and V. Kumar, “Data Guided Discovery of Dynamic Climate Dipoles.,” presented at the CIDU, 2011, pp. 30–44.