Tensions between the diffuse gamma-ray sky observed by the Fermi Large Area Telescope (LAT) and the diffuse high-energy neutrino sky detected by the IceCube South Pole Neutrino Observatory question our knowledge about high-energy neutrino sources in the gamma-ray regime. While blazars are among the most energetic persistent particle accelerators in the Universe, studies suggest that they could account for up to for 10-30% of the neutrino flux measured by IceCube. Our recent results highlighted that the associated IceCube neutrinos arrived in a local gamma-ray minimum (dip) of three strong neutrino point-source candidates. We increase the sample of neutrino-source candidates to study their gamma-ray light curves. We generate the one-year Fermi-LAT light curve for 8 neutrino source candidate blazars (RBS 0958, GB6 J1040+0617, PKS 1313-333, TXS 0506+056, PKS 1454-354, NVSS J042025-374443, PKS 0426-380 and PKS 1502+106), centered on the detection time of the associated IceCube neutrinos. We apply the Bayesian block algorithm on the light curves to characterize their variability. Our results indicate that GB6 J1040+0617 was in the phase of high gamma-ray activity, while none of the other 7 neutrino source candidates were statistically bright during the detection of the corresponding neutrinos and that indeed even most of the times neutrinos arrived in a faint gamma-ray phase of the light curves. This suggests that the 8 source-candidate blazars (associated with 7 neutrino events) in our reduced sample are either not the sources of the corresponding IceCube neutrinos, or that an in-source effect (e.g. suppression of gamma rays due to high gamma-gamma opacity) complicates the multimessenger scenario of neutrino emission for these blazars.