I don't trust teleconnections right now, apart from the teleconnection between the ocean and the lunisolar forcing. Think about it ... this is the teleconnection which has been the elephant in the room all this time.
All the other teleconnections I would think are essentially the dog wagging its tail. These work as the equivalent of weaker proxy measures for the impact of ENSO on other phenomena.
Above I also mentioned the MLR approaches used in tidal analysis and prediction.
This is the tidal prediction bible from NOAA, which discusses the linear regression approaches.
I would imagine that much of what I am doing is captured here, such as the biennial modulation leading to splitting of the spectral terms.
I haven't really taken advantage of the spectral frequency fits possible with the ENSO model so far, having preferred to stay in the time domain.