Our attention can be directed to specific locations in our visual field (space-based attention), or to specific objects (object-based attention). However, object-based attention tends to be less pronounced than space-based attention and can vary greatly between individuals. Here we investigated whether the low prevalence of object-based effects is related to variability in the temporal dynamics of attentional selection. We manipulated cue-to-target intervals from 50 to 600 ms in a two-rectangle discrimination task. Space- and object-based effects were measured at the group level and for individual participants. We used bootstrapping to highlight cue-to-target intervals with maximal space- and object-based effects, and fast Fourier transform (FFT) to investigate rhythmic sampling of locations within and between objects. Whereas overall, space-based effects were robust and stable across all cue-to-target intervals for most participants, object-based effects were small and were only found for a small subset of participants in the different cue-to-target intervals. In the frequency domain, only a small number of participants exhibited significant periodicities, prompting the need for further investigation and consideration. Overall, our study suggests variability in the temporal dynamics of object-based effects underlying their low prevalence, a finding that needs to be further investigated in future studies.