Modern nanophotonics has witnessed the rise of electric anapoles, destructive interferences of electric dipoles and toroidal electric dipoles, actively exploited to cancel electric dipole radiation from nanoresonators. However, the inherent duality of Maxwells equations suggests the intriguing possibility of magnetic anapoles, involving a nonradiating composition of a magnetic dipole and a magnetic toroidal dipole. Here, we predict, fabricate and observe experimentally via a series of dark field spectroscopy measurements a hybrid anapole of mixed electric and magnetic character, with all the dominant multipoles being suppressed by the toroidal terms in a nanocylinder. We delve into the physics of such exotic current configurations in the stationary and transient regimes and predict a number of ultrafast phenomena taking place within sub-ps times after the breakdown of the hybrid anapole. Based on the preceding theory, we design a non-Huygens metasurface featuring a dual functionality: perfect transparency in the stationary regime and controllable ultrashort pulse beatings in the transient.