Clear evidence is reported for the first time of a rapid localized reduction of core electron energy diffusivity during the formation of an electron internal-transport barrier. The transition occurs rapidly (similar or equal to3 ms), during a slow (similar or equal to200 ms) self-inductive evolution of the magnetic shear. This crucial observation, and the correlation of the transition with the time and location of the magnetic shear reversal, lend support to models attributing the reduced transport to the local properties of a zero-shear region, in contrast to models predicting a gradual reduction due to a weak or negative shear.