Rod-like colloids in dense solutions perform collective orientational motions under shear flow. The periodic tumbling motions of the director, i.e. the average orientation of the rods, are commonly characterized as kayaking, wagging and flow-aligning, in order of increasing shear rate. Our event-driven Brownian dynamics simulations of rigid spherocylinders reproduce these three distinct director motions, but also clearly show, for the first time, that the individual mesogens are kayaking at all shear rates. The synchrony of the mesogens's motions gradually decreases with increasing shear rate, which at a critical shear rate causes a transition of the apparent collective motion from kayaking to wagging. The rods's persistent kayaking also explains the continuity of the tumbling period at this transition and the smooth change from wagging to flow-aligning observed at higher shear rates.