Here is a post on finding a second mode in the ENSO time series, in addition to the biennial forcing mode

The paper that the analysis aligns well with is

Kim, Kwang-Yul, James J O’Brien, and Albert I Barcilon. “The Principal Physical Modes of Variability over the Tropical Pacific.” Earth Interactions 7, no. 3 (2003): 1–32. --

After having read this paper, I was amazed that it only has 8 citations and those were mainly self-directed. Kim et al are one of the few papers where one finds references to the biennial periodicity of ENSO.