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In this work, the four-component two-particle propagator technique is employed for the calculation of double ionization spectra of the noble gas atoms Ne through Rn. For a correct assignment of the individual final states, inclusion of spin-orbit coupling and electron correlation is mandatory and is accounted for in the framework of the relativistic propagator. It was observed that the $n{s}^{2}n{p}^{4}$(${}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{2,1,0}$, ${}^{1}\phantom{\rule{-0.16em}{0ex}}{D}_{2}$, ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}$) manifolds of all investigated noble gas dications exhibit a clear main-state character with only small admixture from other configurations. This also refers to the $2{s}^{1}2\phantom{\rule{-0.16em}{0ex}}{p}^{5}$(${}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{2,1,0}^{o}$, ${}^{1}\phantom{\rule{-0.16em}{0ex}}{P}_{1}^{o}$) states of Ne${}^{2+}$. In the argon, krypton, and xenon dications, the $n{s}^{1}n{p}^{5}$(${}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{2,1,0}^{o}$) states, and especially the $n{s}^{1}\phantom{\rule{-0.16em}{0ex}}n{p}^{5}$(${}^{1}\phantom{\rule{-0.16em}{0ex}}{P}_{1}^{o}$) ones, lose intensity due to pronounced configuration interaction. These states experience strong mixings with ground-state shake-up satellites, which occupy the same energy region. The composition of the $5{s}^{1}5{p}^{5}$(${}^{1}\phantom{\rule{-0.16em}{0ex}}{P}_{1}^{o}$) singlet state of Xe${}^{2+}$ is studied in detail by analyzing the corresponding eigenvector. As long as a $LS$ coupling picture can be approximately maintained, the amount of singlet-triplet splitting decreases in the sequence from neon to xenon. In the $6{s}^{1}6{p}^{5}$ manifold of Rn${}^{2+}$, a complete disappearance of well-defined main states takes place leading to a dense and complicated spectrum governed by very strong multiconfiguration effects. Relativistic corrections to the Coulomb interaction are accounted for by inclusion of the Gaunt (magnetic) term.