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Utilising JWST, ALMA and the VLA we present high angular resolution (0.06''- 0.42''), multi-wavelength (4 micron - 3cm) observations of the VLA 1623-2417 protostellar system to characterise the origin, morphology and, properties of the continuum emission. JWST observations at 4.4 micron reveal outflow cavities for VLA 1623 A and, for the first time, VLA 1623 B, as well as scattered light from the upper layers of the VLA 1623 W disk. We model the millimetre-centimetre spectral energy distributions to quantify the relative contributions of dust and ionised gas emission, calculate dust masses, and use spectral index maps to determine where optical depth hinders this analysis. In general, all objects appear to be optically thick down to ~90 GHz, show evidence for significant amounts (10's - 100's M_Earth) of large (>1 mm) dust grains, and are dominated by ionised gas emission for frequencies ~<15 GHz. In addition, we find evidence of unsettled millimetre dust in the inclined disk of VLA 1623 B possibly attributed to instabilities within the circumstellar disk, adding to the growing catalogue of unsettled Class 0/I disks. Our results represent some of the highest resolution observations possible with current instrumentation, particularly in the case of the VLA. However, our interpretation is still limited at low frequencies (~<22 GHz) and thus motivates the need for next-generation interferometers operating at centimetre wavelengths., Comment: Accepted for publication in ApJ. 35 pages, 10 figures