This paper presents an N-ary Gaussian Model for predicting endpoint distributions in pointing tasks across task scenarios. Built on the foundational principles of the Ternary Gaussian model series, our model framework allows researchers to define parameter constraints and automatically refine model combinations, eliminating the need for predefined equations based on data analysis. We utilize the Bayesian Information Criterion (BIC) for model selection, ensuring simplicity while maintaining predictive accuracy. We conducted a comparative analysis against published baselines across 7 diverse datasets, covering 1D, 2D, and 3D tasks, different input modalities, different display devices, and time-constrained scenarios, demonstrating the robustness and generalization of the N-ary Gaussian Model. The N-ary Gaussion model offers an automated solution for modeling pointing uncertainty, and also incorporates cross output device, input modality, and temporal constraint factors into spatial pointing uncertainty modeling for the first time.