The majority of galaxy mergers are expected to be minor mergers . The observational signatures of minor mergers are not well understood , thus there exist few constraints on the minor merger rate . This paper seeks to address this gap in our understanding by determining if and when minor mergers exhibit disturbed morphologies and how they differ from the morphology of major mergers . We simulate a series of unequal-mass moderate gas-fraction disc galaxy mergers . With the resulting g -band images , we determine how the time-scale for identifying galaxy mergers via projected separation and quantitative morphology ( the Gini coefficient G , asymmetry A , and the second-order moment of the brightest 20 % of the light M _ { 20 } ) depends on the merger mass ratio , relative orientations and orbital parameters . We find that G - M _ { 20 } is as sensitive to 9:1 baryonic mass ratio mergers as 1:1 mergers , with observability time-scales \sim 0.2 - 0.4 Gyr . In contrast , asymmetry finds mergers with baryonic mass ratios between 4:1 and 1:1 ( assuming local disc galaxy gas-fractions ) . Asymmetry time-scales for moderate gas-fraction major disc mergers are \sim 0.2 - 0.4 Gyr , and less than 0.06 Gyr for moderate gas-fraction minor mergers . The relative orientations and orbits have little effect on the time-scales for morphological disturbances . Observational studies of close pairs often select major mergers by choosing paired galaxies with similar luminosities and/or stellar masses . Therefore , the various ways of finding galaxy mergers ( G - M _ { 20 } , A , close pairs ) are sensitive to galaxy mergers of different mass ratios . By comparing the frequency of mergers selected by different techniques , one may place empirical constraints on the major and minor galaxy merger rates .