Atypical Trigeminal Neuralgia (ATN) represents a debilitating, refractory chronic pain condition often resistant to pharmacological management, necessitating deep-brain stimulation techniques that traditionally require invasive neurosurgical leads. To address the critical need for non-invasive, timely intervention, this study used the SIMNIBS 4.5 finite-element analysis pipeline to computationally validate Temporal interference (TI) stimulation as the actuator stage of a novel sensor-driven, closed-loop neuromodulation system. Using a high-resolution anatomical head phantom, the authors modelled a specialized infraorbital-occipital electrode montage designed to steer the interference envelope to the skull base geometrically. The simulation applied a 2 kHz and 2.005 kHz carrier frequency paradigm to generate a therapeutic 5Hz beat at the Trigeminal Ganglion (TG) integrated within a theoretical control framework proposed to be triggered by physiological biomarkers of pain, including Heart Rate Variability (HRV) and Electrodermal Activity (EDA). Results demonstrated a successful focal intersection at the petrous apex, achieving a suprathreshold TI envelope magnitude of 0.36V/m within the target ganglion while minimizing superficial cortical exposure. Furthermore, safety analysis confirmed a peak Specific Absorption Rate (SAR) of 0.14 W/Kg, significantly below the 2.0 W/Kg ICNIRP limit. These findings validate the biophysical feasibility of TI to non- invasively engage deep cranial nerves, supporting the development of responsive, closed-loop therapeutic architectures for refractory ATN.