  Theoretical models are vital for exploring the galaxy merger process, which
plays a crucial role in the evolution of galaxies. Recent advances in modelling
have placed tight constraints on the buildup of stellar material in galaxies
across cosmic time. Despite these successes, extracting the merger rates from
observable data remains a challenge. Differences in modelling techniques,
combined with limited observational data, drive conflicting conclusions on the
merging timescales of close pairs. We employ an empirical model for galaxy
formation that links galaxy properties to the growth of simulated dark matter
halos, along with mock lightcone galaxy catalogues, to probe the dependencies
of pair merging probabilities and merging timescales. In this work, we
demonstrate that the pair merging probabilities are best described by a
logistic function and that mean merging timescales can be well approximated by
a linear relation in the projected separation and line of sight velocity
difference in observed pairs. Together, our fitting formulae can accurately
predict merger rates from galaxy pairs to at least $z\sim4$ under a wide
variety of pair selection criteria. Additionally, we show that some commonly
used pair selection criteria may not represent a suitable sample of galaxies to
reproduce underlying merger rates. Finally, we conclude from our analysis that
observation timescales are primarily driven by dynamics and are not strongly
impacted by the star formation properties of the component galaxies.
