The basal ganglia (BG) are a set of interconnected subcortical nuclei that form different feedback loops with cortex and thalamus. Within the BG, the globus pallidus pars externa (GPe) plays a major role for neural dynamics due to its dense coupling with other major BG structures. In Parkinson’s disease (PD), hyper-synchronized, oscillatory neural activity has been reported throughout the BG. This has in part been attributed to changes in the dynamic regime of the feedback loop formed by subthalamic nucleus (STN) and GPe. That is, mechanistic explanations have been provided how the interplay between excitatory (STN) and inhibitory signalling (GPe) can promote neural oscillations that are transmitted throughout BG and cortex. These theories assume a homogeneous organization of both STN and GPe. However, convincing evidence has been gathered from animal experiments that demonstrate the existence of distinct cell types inside GPe with different projection targets. While prototypical GPe cells project provide the major source of feedback to the STN, arkypallidal GPe cells provide feedback to the striatum. Whether GPe afferents express a similar form of cell type selectivity is unclear at this point. Furthermore, it is not known which role the different cell types play for GPe intrinsic activity. In this work, we investigate the impact of GPe-intrinsic connectivity on its dynamic regimes via computational modeling and bifurcation analysis. Using a mean-field model of a spiking neural network, we find that different coupling patterns between and within prototypical and arkypallidal cells situate the GPe nearby different bifurcation points that lead to distinct responses to extrinsic input. We demonstrate under which conditions selective vs. non-selective inputs to prototypical and arkypallidal cells can induce phase transitions inside GPe. Based on these findings, we generate hypotheses of how changes to GPe-internal structure can promote oscillatory activity in PD.