When rocket engine nozzles operate at a high degree of over-expansion, an internal flow separation occurs with a strong unsteady shock–wave boundary layer interaction. The global dynamics results in a low-frequency mode, which is associated with the shock displacement, and a high-frequency mode, which is correlated with the shear layer–boundary layer interaction. While the mechanism responsible for the low-frequency oscillation is known, the one in charge of the high-frequency unsteadiness is not yet clear. The scope of this paper is to provide a physical explanation for this mechanism. To do that, a delayed detached eddy simulation is used to numerically reproduce the flow in the case of a sub-scale cold-gas truncated ideal contour nozzle. The obtained results are successfully compared to the experiments and confirm the presence of two non-axisymmetric wall pressure signatures at Strouhal numbers St=fDj/Uj≃0.2 and 0.3 with different azimuthal selections. To reveal the origin of such modes, a power spectral density analysis is performed in the separated region. The analysis shows that both modes originate from the external shear layer and behave as “twins” in the separated region. The reason is that both modes are two sides of the same impinging shear layer instability: the acoustic mode propagates with the sound velocity, while the hydrodynamic one propagates with the supersonic shear layer velocity. In this context, the resulting self-sustained dynamics may be due to an acoustic–hydrodynamic feedback loop involving the impinging shear layer instability of the external supersonic shear layer and the separated region.