There is SOI data on a daily time scale since 1992 on this site https://data.longpaddock.qld.gov.au/SeasonalClimateOutlook/SouthernOscillationIndex/SOIDataFiles/DailySOI1887-1989Base.txt
I had been using monthly data and it wasn't clear whether the high wave-number (high-K) amplitudes used to fit the monthly time-series would also be apparent on a daily basis. Keeping the filtering to a minimum, the upper panel shows the monthly SOI time-series, applying a fit from 1992 onward. The bottom panel shows what it looks like on a magnified daily time scale.
The recent paper by Jajcay (cite below) claims that there is synchronization across time scales for ENSO, which is implicit for the ENSO model used above. For our ENSO model, the low -K solutions (low frequency, corresponding to the main Tahiti-Darwin standing wave dipole) are automatically synchronized with the high-K solutions (high frequency, which are likely related to Tropical Instability Waves and/or Madden-Julian Oscillations). The main dipole requires both the low-K and high-K solutions to achieve the sharp jagged profile -- constructed through the superposition of the non-linear harmonics -- which is clearly apparent when one expands to the daily time-scale. For example, the strong 1998 El-Nino is actually composed of the superposition of a longer-time-period signal superposed with multiple higher-frequency jagged peaks.
> Jajcay, Nikola, et al. ["Synchronization and causality across time scales in El Niño Southern Oscillation."](https://www.nature.com/articles/s41612-018-0043-7) npj Climate and Atmospheric Science 1.1 (2018): 33.