Radioactive ^{136}Te has two valence protons and two valence neutrons outside of the ^{132}Sn double shell closure, providing a simple laboratory for exploring the emergence of collectivity and nucleon-nucleon interactions. Coulomb excitation of ^{136}Te on a titanium target was utilized to determine an extensive set of electromagnetic moments for the three lowest-lying states, including B(E2;0_{1}^{+}→2_{1}^{+}), Q(2_{1}^{+}), and g(2_{1}^{+}). The results indicate that the first-excited state, 2_{1}^{+}, composed of the simple 2p⊕2n system, is prolate deformed, and its wave function is dominated by excited valence neutron configurations, but not to the extent previously suggested. It is demonstrated that extreme sensitivity of g(2_{1}^{+}) to the proton and neutron contributions to the wave function provides unique insight into the nature of emerging collectivity, and g(2_{1}^{+}) was used to differentiate among several state-of-the-art theoretical calculations. Our results are best described by the most recent shell model calculations.