We report on the β-delayed neutron emission probability (P 1n) measurements of the 82,83,84 Ga (N = 51,52,53) precursors performed in one single experiment using the 3 He neutron-counter TETRA at the ALTO facility in Orsay. Altogether our results for the three A = 82,83, and 84 Ga precursors point towards a sizable P 1n staggering in the N = 50 region, similar to the one already observed just after the N = 28 shell closure in the K isotopes chain, hinting at a similar mechanism. We will discuss the possible microscopic origin of this behavior, i.e., the existence in the light N = 51 isotones of low-lying components of the so called pygmy Gamow-Teller resonance, already well established at Z = 36, and persisting toward 79 Ni.