In the analysis of human motor skills, tracking tasks with multisine target signals are often performed as they allow for quantitative measurement, identification, and modeling of human control dynamics. In this paper, the same "cybernetic" approach is taken to analyze eye movement dynamics in gaze tracking tasks, where participants had to track a moving target marker across the screen) with their eyes (i.e., a eye-only task) and 2) with their dominant hand (i.e., a eye-hand task). A human-in-the-loop experiment with 10 participants was performed to measure the eye movement dynamics. These two different conditions were performed with four different bandwidths of the multisine target signal driving the movement of the visual stimulus. The results show that the measured eye movement dynamics can be identified from the data of all experiment conditions and can be accurately modeled as an underdamped mass-spring-damper system with a time delay. Furthermore, with increased target signal bandwidth the bandwidth of participants' eye movements also increases. Future development of gaze tracking tasks into a new tool for assessment of altered gaze behavior due to neurological diseases should take the balance between saccadic and smooth pursuit eye movements into account and avoid very high (i.e., too difficult) bandwidths to warrant accurate modelling of gaze dynamics.