We show that the blazar PKS 1424+240, which has been recently associated by IceCube with a neutrino excess at the 3.3 𝜎 level together with three other sources, is similar to the first plausible non-stellar neutrino source, TXS 0506+056, in being also a masquerading BL Lac object, i.e., intrinsically a flat-spectrum radio quasar with hidden broad lines and a standard accretion disk. We point out that these two sources share other properties, including spectral energy distribution, high powers, parsec scale properties, and possibly radio morphology. We speculate that the relatively rare combination of proton-loaded jets, possibly typical of high-excitation sources, and efficient particle acceleration processes, related to their relatively high synchrotron peak frequencies, might favour neutrino production in these two sources. GB6 J1542+6129, which has also recently appeared twice in a list of IceCube associations, seems also to belong to this rare blazar sub-class, which includes at most ≈ 20 Fermi-4LAC blazars.