Symbiotic stars are binaries in which a cool and evolved star of luminosity class I-III accretes onto a smaller companion. However, direct accretion signatures like disc flickering and boundary layer X-rays are typically outshone or suppressed by the luminous giant, shell burning on the accreting white dwarf, and the illuminated wind nebula. We present a new way to find symbiotics that is less biased against directly-detectable accretion discs than methods based on narrow-band H$\alpha$ photometry or objective prism plate surveys. We identified outliers in SkyMapper survey photometry, using reconstructed uvg snapshot colours and rapid variability among the three exposures of each 20-minute SkyMapper Main Survey filter sequence, from a sample of 366,721 luminous red objects. We found that SkyMapper catalog colours of large-amplitude pulsating giants must be corrected for variability, and that flickering is detectable with only three data points. Our methods probed a different region of parameter space than a recent search for accreting-only symbiotics in the GALAH survey, while being surprisingly concordant with another survey's infrared detection algorithm. We discovered 12 new symbiotics, including four with optical accretion disc flickering. Two of the optical flickerers exhibited boundary-layer hard X-rays. We also identified 10 symbiotic candidates, and discovered likely optical flickering in the known symbiotic V1044 Cen (CD-36 8436). We conclude that at least 20% of the true population of symbiotics exhibit detectable optical flickering from the inner accretion disc, the majority of which do not meet the H$\alpha$ detection thresholds used to find symbiotics in typical narrow-band surveys.