Although KamLAND apparently rules out Resonant-Spin-Flavor-Precession (RSFP) as an explanation of the solar neutrino deficit, the solar neutrino fluxes in the Cl and Ga experiments appear to vary with solar rotation. Added to this evidence, summarized here, a power spectrum analysis of the Super-Kamiokande data reveals significant variation in the flux matching a dominant rotation rate observed in the solar magnetic field in the same time period. Three frequency peaks, all related to this rotation rate, can be explained quantitatively. A Super-Kamiokande paper reported no time variation of the flux, but showed the same peaks, there interpreted as statistically insignificant, due to an inappropriate analysis. This modulation is small (7%) in the Super-Kamiokande energy region (and below the sensitivity of the Super-Kamiokande analysis) and is consistent with RSFP as a subdominant neutrino process in the convection zone. The data display effects that correspond to solar-cycle changes in the magnetic field, typical of the convection zone. This subdominant process requires new physics: a large neutrino transition magnetic moment and a light sterile neutrino, since an effect of this amplitude occurring in the convection zone cannot be achieved with the three known neutrinos. It does, however, resolve current problems in providing fits to all experimental estimates of the mean neutrino flux, and is compatible with the extensive evidence for solar neutrino flux variability.