We analyze spontaneous oscillations in a second-order delayed-feedback shunting model of the pupil light reflex. This model describes in a simple fashion the nonlinear effects of both the iris and retinal parts of the reflex pathway. In the case of smooth negative feedback, linear stability analysis is used to determine the conditions for a Hopf bifurcation in the pupil area as a function of various neurophysiological parameters of the system such as the time delay and the strength of neural connections. We also investigate oscillation onset in the case of piecewise negative feedback and obtain an analytical expression for the period of oscillations. Finally, complex periodic behavior is shown to arise in the presence of mixed feedback.