Interaction-powered supernovae (SNe) explode within an optically thick circumstellar medium (CSM) that could be ejected during eruptive events. To identify and characterize such pre-explosion outbursts, we produce forced-photometry light curves for 196 interacting SNe, mostly of Type IIn, detected by the Zwicky Transient Facility between early 2018 and 2020 June. Extensive tests demonstrate that we only expect a few false detections among the 70,000 analyzed pre-explosion images after applying quality cuts and bias corrections. We detect precursor eruptions prior to 18 Type IIn SNe and prior to the Type Ibn SN 2019uo. Precursors become brighter and more frequent in the last months before the SN and month-long outbursts brighter than magnitude -13 occur prior to 25% (5-69%, 95% confidence range) of all Type IIn SNe within the final three months before the explosion. With radiative energies of up to 10(49) erg, precursors could eject similar to 1 M of material. Nevertheless, SNe with detected precursors are not significantly more luminous than other SNe IIn, and the characteristic narrow hydrogen lines in their spectra typically originate from earlier, undetected mass-loss events. The long precursor durations require ongoing energy injection, and they could, for example, be powered by interaction or by a continuum-driven wind. Instabilities during the neon- and oxygen-burning phases are predicted to launch precursors in the final years to months before the explosion; however, the brightest precursor is 100 times more energetic than anticipated.