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X-ray eclipse mapping is a promising modelling technique, capable of constraining the mass and/or radius of neutron stars (NSs) or black holes (BHs) in eclipsing binaries and probing any structure surrounding the companion star. In eclipsing systems, the binary inclination, $i$, and mass ratio, $q$ relate via the duration of totality, $t_{e}$. The degeneracy between $i$ and $q$ can then be broken through detailed modelling of the eclipse profile. Here we model the eclipses of the NS low-mass X-ray binary Swift J1858.6$-$0814 utilising archival NICER observations taken while the source was in outburst. Analogous to EXO 0748$-$676, we find evidence for irradiation driven ablation of the companion's surface by requiring a layer of stellar material to surround the companion star in our modelling. This material layer extends $\sim 7000 - 14000$ km from the companion's surface and is likely the cause of the extended, energy-dependent and asymmetric ingress and egress that we observe. Our fits return an inclination of $i \sim 81^{\circ}$ and a mass ratio $q \sim 0.14$. Using Kepler's law to relate the mass and radius of the companion star via the orbital period ($\sim$ 21.3 hrs), we subsequently determine the companion to have a low mass in the range $0.183 M_{\odot} \leq M_{cs} \leq 0.372 M_{\odot}$ and a large radius in the range $1.02 R_{\odot} \leq R_{cs} \leq 1.29 R_{\odot}$. Our results, combined with future radial velocity amplitudes measured from stellar absorption/emission lines, can place precise constraints on the component masses in this system.