This work presents a systematic shell-model investigation of light nuclei \(^{3}\text{He}\) , \(^{4}\text{He}\) , \(^{6}\text{He}\) , and \(^{6}\text{Li}\) using both a core-based configuration (with \(^{4}\text{He}\) treated as an inert core in the psd model space) and an extended large-basis framework (within the spsdpf shell-model space). A wide range of observables is studied, including root-mean-square charge radii, magnetic dipole and electric quadrupole moments, excitation energy spectra, and an extensive set of electromagnetic form factors. The latter include longitudinal Coulomb (C0, C2), transverse multipoles (M1, E2, M3), and the longitudinal C2 form factor contains a weak contribution associated with convection current effects. The extended spsdpf shell-model space combined with realistic Skyrme-type and Woods–Saxon potentials generally provides the best agreement with experiment, successfully reproducing diffraction minima and high-q behavior of the C0 and C2 form factors in \(^{6}\text{Li}\) and capturing halo-like extensions in \(^{6}\text{He}\) . Multipole decompositions for the \(2^+\) and \(3^+\) states of \(^{6}\text{Li}\) show a dominant M3 contribution in the extended description, contrasting with mixed E2+M3 dominance in the core-based model. The transverse M1 response of the \(0^+\) and \(1^+\) states displays an unusual dependence on the harmonic oscillator basis, while the longitudinal C2 form factor of the \(2^+\) (5.37 MeV) state is examined for the first time and found to constrain convection-current contributions. These results demonstrate that realistic interactions in extended shell-model spaces provide the most predictive description of light nuclei, while comparison with core-based truncations clarifies the roles of configuration mixing, clustering, and radial wave functions in shaping electromagnetic observables.
