The chemical bonding schemes of thallium cluster anions commonly comply with neither Wade-Mingos's rules nor the Zintl-Klemm concept and thus far have escaped a fully consistent description. In general, the number of electrons available for the cluster skeleton bonding fall below those required according to the qualitative concepts mentioned and the clusters were labeled "hypoelectronic". Based on fully relativistic band structure calculations on respective complete extended solids and electronic structure calculations on excised, charge compensated, and geometrically optimized clusters, we have identified two mechanisms that are suited to lift the degeneracy of partially filled electronic states and to open a HOMO-LUMO gap, the Jahn-Teller effect and relativistic spin-orbit coupling. Treatment on this level of theory shows that, in accordance with experiment, the thallium cluster anions known are electronically saturated and not deficient in valence electrons. We provide qualitative group theoretical procedures for analyzing the Jahn-Teller effect and spin-orbit coupling in lifting the degeneracy of frontier orbitals in highly symmetric thallium cluster anions.