Dilemma zones at signalized intersections present a commonly occurring but unsolved challenge for both drivers and traffic operators. Onsets of the yellow lights prompt varied responses from different drivers: some may brake abruptly, compromising the ride comfort, while others may accelerate, increasing the risk of red-light violations and potential safety hazards. Such diversity in drivers' stop-or-go decisions may result from not only surrounding traffic conditions, but also personalized driving behaviors. To this end, identifying personalized driving behaviors and integrating them into advanced driver assistance systems (ADAS) to mitigate the dilemma zone problem presents an intriguing scientific question. In this study, we employ a game engine-based (i.e., CARLA-enabled) driving simulator to collect high-resolution vehicle trajectories, incoming traffic signal phase and timing information, and stop-or-go decisions from four subject drivers in various scenarios. This approach allows us to analyze personalized driving behaviors in dilemma zones and develop a Personalized Transformer Encoder to predict individual drivers' stop-or-go decisions. The results show that the Personalized Transformer Encoder improves the accuracy of predicting driver decision-making in the dilemma zone by 3.7% to 12.6% compared to the Generic Transformer Encoder, and by 16.8% to 21.6% over the binary logistic regression model.