Concolic testing for deep neural networks alternates concrete execution with constraint solving to search for inputs that flip decisions. We present an {influence-guided} concolic tester for Transformer classifiers that ranks path predicates by SHAP-based estimates of their impact on the model output. To enable SMT solving on modern architectures, we prototype a solver-compatible, pure-Python semantics for multi-head self-attention and introduce practical scheduling heuristics that temper constraint growth on deeper models. In a white-box study on compact Transformers under small $L_0$ budgets, influence guidance finds label-flip inputs more efficiently than a FIFO baseline and maintains steady progress on deeper networks. Aggregating successful attack instances with a SHAP-based critical decision path analysis reveals recurring, compact decision logic shared across attacks. These observations suggest that (i) influence signals provide a useful search bias for symbolic exploration, and (ii) solver-friendly attention semantics paired with lightweight scheduling make concolic testing feasible for contemporary Transformer models, offering potential utility for debugging and model auditing.