Eye movements are the result of complex interactions between cortical and sub-cortical regions. Consequently, they are considered as an important bio-marker for neurological function. Attempts to construct an oculomotor model rely on classic paradigms. In this research, a cybernetic approach was used to construct and examine a novel paradigm, which can be used as a new tool to quantify and classify neurodegeneration. Young, healthy adults (N = 24) participated in a quasi-random gaze pursuit tracking task to investigate horizontal and vertical gaze behavior in one- and two-dimensional tracking. Results indicate different horizontal gaze in terms of performance (13% and 23% better) and model parameters (5.6% and 10.2% higher Kg, 6.6% and 7.6% lower τg), comparing the 1D conditions and horizontal and vertical direction in the 2D condition, respectively. Vertical gaze due to cross-feed was observed up to 3 rad/s in presence of a horizontally moving target stimulus, varying in magnitude between subjects. For the proposed paradigm, an increased target signal bandwidth should be used, such that neuromuscular gaze dynamics can be captured as well, as these parameters are known to relate to neurodegeneration.