An equimolar mixture of a cationic surfactant, cetylperidinium chloride (CPyCl), and salt sodium salicylate (NaSal) forms wormlike micelles in aqueous solutions. Under shear, the solution shows a pronounced shear-thickening behavior, which is coupled with oscillations in shear rate and the apparent viscosity. In this shear-thickening regime shear bands form, which also oscillate in position and intensity. These shear bands are visualized by direct imaging and Rheo-small angle light scattering methods. Temporal intensity fluctuations of the shear bands were evaluated using image analysis. Fourier transformations (FT) of the oscillating shear rate and intensity of the shear bands showed a single dominating frequency in the power spectrum analysis. This characteristic frequency as well as the amplitude of shear rate fluctuation was found to increase with stress. From the rheological and optical measurements, we propose that a stress driven mechanism is responsible for the formation of shear bands. Experiments performed in transparent parallel-plate geometry show dampening of the shear rate oscillations and increase in the characteristic frequency with decrease in the gap. Power spectrum analysis and the SALS measurements confirm the formation of different structures as a function of gap size in the parallel-plate geometry.