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One of the most intriguing mechanisms underlying symmetry breaking and pattern formation is the phenomenon of Turing instabilities. These self-organizing spatial structures emerge from the interaction of at least two diffusive species under specific conditions. Turing's ideas have been extensively employed in the specialized literature to elucidate developmental patterns and inform synthetic biology design. In this study, we investigate a previously proposed morphogenetic synthetic circuit comprising two genes regulated by an identical control system. The spatially homogeneous version of this simple model exhibits a rich phase diagram, featuring a saddle-node bifurcation, spirals, and limit cycles. Linear stability analysis and numerical simulations of the complete model enable us to determine the conditions conducive to Turing pattern formation, as well as transient patterns. Our findings indicate that the parameter region yielding Turing patterns is significantly smaller than that producing transient patterns. Furthermore, we observe that the temporal evolution towards Turing patterns can exhibit one or two distinct length scales, contingent upon initial conditions. Notably, we identify a parameter region where the persistence time of transient patterns depends on the distance between the system's operating parameters and the Turing pattern boundary. This persistence time exhibits a singularity at a critical distance, giving rise to metastable patterns. To the best of our knowledge, transient and metastable patterns associated with Turing instabilities have not been previously reported in morphogenetic models.