In this paper we studied the behavior of a model of a periodically driven photosensitive Belousov-Zhabotinsky reaction. The computations were carried out with a two-variable Oregonator model modified to account for photosensitivity. The external light intensity was periodically switched between two levels. By keeping the total cycle length fixed while varying the duration of the positive and negative perturbations, a variety of dynamical behaviors can be observed, including phase locking, torus oscillations, periodic transitions, and chaos. The results suggest that not only are the forcing frequency and amplitude important, as was already known, but the detailed waveform of the external forcing is also essential in determining the behavior of a driven dynamical system. Two scenarios have been investigated in this study: (a) the system was driven between two limit cycles; (b) the system was driven between excitable and oscillatory;states. Random modulation of the durations of the positive and negative perturbations (low and high illumination states) leads to synchronization of complex behavior. Calculating the leading Lyapunov exponent confirms that this form of random driving may be used to suppress chaotic behavior.