Multi-phase Gaussian fit of the [Ne III], H₂S(1), [O III]λ5007, and CO (2-1) emission lines from MIRI/MRS, MUSE, and ALMA data cubes, respectively. Top left panel: [Ne III] emission tracing the redshifted ionised gas, obtained collapsing the flux in the spectral window 15.56–15.57 μm rest-frame from the PSF subtracted data cube (see Appendix A). White contours represent arbitrary [OIII] flux levels from MUSE data. North is up and east is left. Top right panels: Integrated [Ne III] and H₂S(1) emission extracted from the black circular aperture of radius 0.6″, shown on the left panel. Bottom left: Integrated [O III]λ5007 emission and best-fit extracted from the same aperture shown in the top left panel. Bottom right: Integrated CO (2-1) emission extracted from spaxels with S/N ≥ 3, covering the nuclear region of NGC 424, as is shown in the bottom panel of Fig. 4. Data and total best-fit model are in black and red, respectively. The sum of the single Gaussian best-fit components is shown in blue (narrow), and orange (broad). Bottom panels show the residuals in green. Vertical dashed grey lines mark the rest-frame wavelength of the transitions. Data and best-fit are normalised to the peak of the observed spectrum.