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Ultra-fast and multi-dimensional spectroscopy gives a powerful looking glass into the dynamics of molecular systems. In particular two-dimensional electronic spectroscopy (2DES) provides a probe of coherence and the flow of energy within quantum systems which is not possible with more conventional techniques. While heterodyne-detected (HD) 2DES is increasingly common, more recently fluorescence-detected (FD) 2DES offers new opportunities, including single-molecule experiments. However in both techniques it can be difficult to unambiguously identify the pathways which dominate the signal. Therefore the use of numerically modelling of 2DES is vitally important, which in turn requires approximating the pulsing scheme to some degree. Here we employ non-pertubative time evolution to investigate the effects of finite pulse width and amplitude on 2DES signals. In doing so we identify key differences in the response of HD and FD detection schemes, as well as the regions of parameter space where the signal is obscured by unwanted artefacts in either technique. Mapping out parameter space in this way provides a guide to choosing experimental conditions and also shows in which limits the usual theoretical approximations work well and which limits more sophisticated approaches are required.