In lyotropic liquid crystalline polymers, flow is known to induce either director tumbling or flow alignment, depending on the shear rate. Recently the existence of an intermediate transition region, a "wagging" regime, has been predicted on the basis of molecular theories. Here, rheological and rheo-optical techniques have been applied to assess the physical reality of the wagging regime in a solution of poly(benzyl glutamate). Stationary rheological and rheo-optical characteristics indicate a gradual change from tumbling to flow aligning when the shear rate is increased, without any divergent behavior in between. When transient measurement techniques are used, however, distinct differences can be observed over a very narrow shear rate range, immediately before the onset of flow alignment. This intermediate region is characterized by strongly fluctuating transients of the stresses and the linear conservative dichroism, especially when starting from a flow-aligned initial condition. In this manner evidence is provided for the existence of an intermediate regime, which can be associated with the predicted wagging regime.