Spin-orbit coupling for an electron in 5d orbitals is as large as 0.5 eV, and gives rise to the formation of spin-orbital entangled objects, characterized by the effective total angular momentum Jeff. Of particular interest are the Jeff = 3/2 states realized in 5d 1 transition metal ions surrounded by an anion octahedron. The pure Jeff = 3/2 quartet does not have any magnetic dipolar moment ( = 0) but hosts hidden pseudo-dipolar moments accompanied by charge quadrupoles and magnetic octupoles. Promising materials to realize such physics include Cs2TaCl6 and Rb2TaCl6, which are correlated insulators with 5d 1 Ta 4+ ions in a regular Cl octahedron. Here we demonstrate that these Ta chlorides have a substantially suppressed effective magnetic dipolar moment of ~ 0.2 B and behave almost like a non-magnetic insulator. The four-fold degeneracy of Jeff = 3/2 is lifted only at low temperatures due to the ordering of charge quadrupolar and pseudo-dipolar moments. While the transition is not magnetically pronounced, it can be observed due to recovery of the full Rln4 entropy.