We report the first systematic investigation of the phenomenon of “switching” between the two bistable axial jet (AJ) and precessing jet (PJ) flow modes in the fluidic precessing jet (FPJ) nozzle. While geometric configurations have been identified where the fractional time spent in the AJ mode is much less than that in the PJ mode, nevertheless, the phenomenon is undesirable and also remains of fundamental interest. This work was undertaken numerically using the unsteady shear stress transport (SST) model, the validation of which showed a good agreement with the experimental results. Three methods were employed in the current work to trigger the flow to switch from the AJ to the PJ modes. It is found that some asymmetry in either the inlet flow or the initial flow field is necessary to trigger the mode switching, with the time required to switch being dependent on the extent of the asymmetry. The direction and frequency of the precession were found to depend on the direction and intensity of the imposed inlet swirling, which will be conducive to the control of the FPJ flow for related industrial applications and academic research. The process with which the vortex skeleton changes within the chamber is also reported. Furthermore, both the rate of spreading and the maximum axial velocity decay of the jet within the nozzle are found to increase gradually during the switching process from the AJ to the PJ modes, consistent with the increased curvature within the local jet.