Robotic vision introduces requirements for real-time processing of fast-varying, noisy information in a continuously changing environment. In a real-world environment, convenient assumptions, such as static camera systems and deep learning algorithms devouring high volumes of ideally slightlyvarying data are hard to survive. Leveraging on recent studies on the neural connectome associated with eye movements, we designed a neuromorphic oculomotor controller and placed it at the heart of our in-house biomimetic robotic head prototype. The controller is unique in the sense that (1) all data are encoded and processed by a spiking neural network (SNN), and (2) by mimicking the associated brain areas' topology, the SNN is biologically interpretable and requires no training to operate. Here, we report the robot's target tracking ability, demonstrate that its eye kinematics are similar to those reported in human eye studies and show that a biologically-constrained learning, although not required for the SNN's function, can be used to further refine its performance. This work aligns with our ongoing effort to develop energy-efficient neuromorphic SNNs and harness their emerging intelligence to control biomimetic robots with versatility and robustness.