We present and discuss accurate and densely mapped BVR_C_I_C_ light curves of the neon Nova Mon 2012, supplemented by the evolution in Stromgren b and y bands and in the integrated flux of relevant emission lines. Our monitoring started with the optical discovery of the nova (50days past the first detection in gamma-rays by Fermi-LAT) and extend to day +270, well past the end of the super-soft phase in X-rays. The nova was discovered during the nebular decline, well past t_3_ and the transition to optically thin ejecta. It displayed very smoothly evolving light curves. A bifurcation between y and V light curves took place at the start of the super-soft X-ray source (SSS) phase, and a knee developed towards the end of the SSS phase. The apparent magnitude of the nova at the unobserved optical maximum is constrained to +3<=V<=4.5. The appearance, grow in amplitude and then demise of a 0.29585 (+/-0.00002) days orbital modulation of the optical brightness was followed along the nova evolution. The observed modulation, identical in phase and period with the analogue seen in the X-ray and satellite ultraviolet, has a near-sinusoidal shape and a weak secondary minimum at phase 0.5. We favour an interpretation in terms of super-imposed ellipsoidal distortion of the Roche lobe filling companion and irradiation of its side facing the WD. Similar light curves are typical of symbiotic stars where a Roche lobe filling giant is irradiated by a very hot WD. Given the high orbital inclination, mutual occultation between the donor star and the accretion disc could contribute to the observed modulation. The optical+infrared spectral energy distribution of Nova Mon 2012 during the quiescence preceding outburst is nicely fitted by an early K-type main-sequence star (~K3V) at 1.5kpc distance, reddened by E(B-V)=0.38, with a WD companion and an accretion disc contributing to the observed blue excess and moderate H{alpha} emission. A typical early K-type main-sequence star with a mass of ~0.75M_{sun}_ and a radius of ~0.8 R{sun} would fill its Roche lobe for a P=0.29585d orbital period and a more massive WD companion (as implied by the large Ne overabundance of the ejecta).