In this experimental and theoretical study, it was found that the emission pattern of the doubly positively charged exciton complex X2+ strongly depends on the nature of the involved excited hole states as well as the quantum dot symmetry. The two-hole system in the final state of the X2+ recombination for the investigated high-symmetry pyramidal InGaAs quantum dots does not exhibit the singlet-triplet like arrangement previously observed for the two-electron counterpart. Instead, the final states exhibit two true doublets, in accordance with group-theoretical predictions. Asymmetry is manifested in the photoluminescence spectra of X2+ by a significant splitting of one doublet, which is a spectral feature exhibited to some degree by all of the measured quantum dots. The analysis demonstrates that an external magnetic field elevates the symmetry of the quantum dots. This work highlights the exciton complex X2+ as a very sensitive probe of the quantum dot shape as well as the nature of the involved quantum states. Thus, its spectral features are very suitable for an efficient uninvasive postgrowth symmetry characterization of quantum dots.