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Following the discovery of SAGE0536AGN ($z \sim$ 0.14), with the strongest 10-$μ$m silicate emission ever observed for an Active Galactic Nucleus (AGN), we discovered SAGE0534AGN ($z \sim$ 1.01), a similar AGN but with less extreme silicate emission. Both were originally mistaken as evolved stars in the Magellanic Clouds. Lack of far-infrared emission, and therefore star-formation, implies we are seeing the central engine of the AGN without contribution from the host galaxy. They could be a key link in galaxy evolution. We used a dimensionality reduction algorithm, t-SNE (t-distributed Stochastic Neighbourhood Embedding) with multi-wavelength data from Gaia EDR3, VISTA survey of the Magellanic Clouds, AllWISE and the Australian SKA Pathfinder to find these two unusual AGN are grouped with 16 other objects separated from the rest, suggesting a rare class. Our spectroscopy at SAAO/SALT and literature data confirm at least 14 of these objects are extragalactic ($0.13 < z < 1.23$), all hosting AGN. Using spectral energy distribution fitter CIGALE we find that the majority of dust emission ($> 70 \%$) in these sources is due to the AGN. Host galaxies appear to be either in or transitioning into the green valley. There is a trend of a thinning torus, increasing X-ray luminosity and decreasing Eddington ratio as the AGN transition through the green valley, implying that as the accretion supply depletes, the torus depletes and the column density reduces. Also, the near-infrared variability amplitude of these sources correlates with attenuation by the torus, implying the torus plays a role in the variability.