Abstract: Fast Radio Bursts (FRBs) represent a novel class of radio transients first reported in 2007. For nearly two decades, astronomers have been investigating their progenitor objects and underlying physical mechanisms. In 2020, the discovery of the low-luminosity FRB 20200428, associated with an X-ray burst from the Galactic magnetar SGR 1935+2154, provided direct evidence linking the origin of FRBs to extreme neutron star or pulsar systems. Despite numerous efforts to identify rotational periodicities in FRBs, no clear signals with high confidence have been detected to date. In this work, based on the potential duty cycles and burst waiting times of repeating FRBs, we propose a novel method to search for periodicities by identifying “periodic gaps” in the waiting time distribution. We apply this technique to four of the most active repeating FRBs: FRB 20121102, FRB 20201124, FRB 20220529, and FRB 20220912. Within a parameter space covering periods from 0.01 s to 300 s and duty cycles from 0 to 0.45, no reliable periodicity was detected. As this range encompasses the vast majority of the Galactic pulsar population, our results suggest significant differences in emission properties (such as duty cycle) between repeating FRBs and Galactic pulsars, thereby imposing new constraints on pulsar/neutron star-related FRB models.