The 2MIG isolated AGNs. 3. Optical--IR variability and dust reverberation in the NLSy1 galaxies Mrk~42 and Mrk~493

This work presents the first dedicated optical–mid-infrared time-domain variability and dust-reverberation analysis of the isolated NLSy1 galaxies Mrk 42 and Mrk 493. We combine ZTF optical light curves, WISE mid-infrared monitoring, archival Swift and SDSS data, and high-cadence IAC80 optical observations. Using colour–magnitude relations, flux–flux analysis, and interpolated cross-correlation functions, we trace variable optical continuum and delayed dust response. Both galaxies show positive optical–MIR lags consistent with dust reverberation. For Mrk 493, we measure an observed-frame g–W1 lag of ${\tau }_{\mathrm{o}\mathrm{b}\mathrm{s}}=79.4\pm 2.2$ d, corresponding to $R_{\mathrm{d}\mathrm{u}\mathrm{s}\mathrm{t}}(W1)\simeq 0.0648$ pc. For Mrk 42, the corresponding lag is ${\tau }_{\mathrm{o}\mathrm{b}\mathrm{s}}=39.1\pm 2.6$ d, giving $R_{\mathrm{d}\mathrm{u}\mathrm{s}\mathrm{t}}(W1)\simeq 0.0320$ pc. These lags provide optical–MIR dust-reverberation radii and BLR–dust scale comparisons for both objects; the resulting $R_{\mathrm{d}\mathrm{u}\mathrm{s}\mathrm{t}}\mathrm{/}{R}_{\mathrm{B}\mathrm{L}\mathrm{R}}$ ratios are $\simeq 6.8$ for Mrk 493 and $\sim 6$–7 for Mrk 42. For Mrk 42, we derive the first host-subtracted AGN continuum luminosity at 5100 Å from SDSS spectral decomposition, giving a self-consistent BLR–dust comparison on an AGN-only luminosity basis. Both galaxies have similar radial hierarchies but different colour behaviour: Mrk 493 shows significant optical and MIR bluer-when-brighter trends, whereas Mrk 42 shows strong optical but weak MIR colour variability. We also identify and analyse a major optical flare in Mrk 42 with four internal maxima spaced by 45–47 d. We interpret this signal as quasi-periodic substructure within a broader accretion-driven flare, rather than as a strictly coherent periodic process. These results indicate that, even in dynamically isolated environments, the variability of low-mass, high-accretion-rate AGNs is governed mainly by the intrinsic state of the accretion flow and its coupling to circumnuclear dust.