Background/Objectives: The ascending pharyngeal artery (APA) exhibits considerable variability in origin. Understanding its anatomy is essential for head and neck surgery, endovascular procedures, and skull base approaches. This study aimed to (1) systematically characterize APA origin sites, (2) evaluate bilateral patterns, and (3) establish a comprehensive sequential classification system for external carotid artery (ECA) branching. Methods: Bilateral computed tomography angiography assessment was performed in 85 patients (170 carotid axes; 54 men, 31 women; mean age 69 ± 10 years). APA origins were classified into six types: Type 0 (absent), Type I (ECA medial wall), Type II (ECA posterior wall), Type III (occipitopharyngeal trunk), Type IV (internal carotid artery), and Type V (other origins). A novel sequential classification system (S-types) documented the complete ECA branching order. Results: APA was absent in 14.71% of cases; APA’s absence or internal carotid origin was noted in 19.41% of cases. Type I occurred in 26.47%, Type II in 35.88%, Type III in 17.06%, Type IV in 4.71%, and Type V in 1.18%. Forty distinct S-types were identified, representing the most comprehensive documentation of ECA branching diversity. No statistically significant side-related (χ2 = 42.12, p = 0.379) or gender-related (χ2 = 49.81, p = 0.138) differences were found. Twenty-three types occurred in fewer than five cases each. Conclusions: This first comprehensive sequential classification system reveals extraordinary anatomical diversity in ECA branching patterns. The absence of predictable side or gender patterns necessitates bilateral preoperative imaging for surgical planning.