In spite of the high-density and strongly correlated nature of the atomic nucleus, experimental and theoretical evidence suggests that around particular 'magic' numbers of nucleons, nuclear properties are governed by a single unpaired nucleon1,2. A microscopic understanding of the extent of this behaviour and its evolution in neutron-rich nuclei remains an open question in nuclear physics 3-5. A textbook example is the electromagnetic moments of indium (Z = 49) 6, which are dominated by a hole with respect to the proton magic number Z = 50 nucleus. They exhibit a remarkably constant behaviour over a large range of odd-mass isotopes, previously interpreted as pure "single-particle behaviour". Here, we present precision laser spectroscopy measurements performed to investigate the validity of this simple single-particle picture. Observation of an abrupt change in the dipole moment at N = 82 reveals that while the single-particle picture indeed dominates at neutron magic number N = 82 2,7, it does not for previously studied isotopes. We present state-of-the-art nuclear theory developed to investigate the details of the nuclear forces that describe the experimental results. The emergence and disappearance of single-particle behaviour was reproduced from an ab initio theory, including challenging many-body correlations in these large, complex nuclei. The inclusion of time-symmetry-breaking mean fields is shown to be essential for a correct description of the nuclear electromagnetic properties within the Density Functional Theory framework. Until now, such time-odd channels have been poorly constrained, but are essential to provide accurate predictions of nuclear properties necessary for searches of new physics with neutrinos 8,9 and studies of fundamental symmetries 10,11. These findings are key to understand the microscopic origin of nuclear electromagnetism and the emergence of single-particle phenomena from complex nuclei.