Traditional phishing detection often overlooks psychological manipulation. This study investigates using Large Language Model (LLM) In-Context Learning (ICL) for fine-grained classification of phishing emails based on a taxonomy of 40 manipulation techniques. Using few-shot examples with GPT-4o-mini on real-world French phishing emails (SignalSpam), we evaluated performance against a human-annotated test set (100 emails). The approach effectively identifies prevalent techniques (e.g., Baiting, Curiosity Appeal, Request For Minor Favor) with a promising accuracy of 0.76. This work demonstrates ICL's potential for nuanced phishing analysis and provides insights into attacker strategies.