Traffic crashes at signalized intersections are frequently linked to driver behavior at the onset of the circular yellow (CY) indication. To better understand behavioral factors that influence a driver’s decision to stop or go at an intersection, this study analyzed the behavior of the driver of a subject vehicle at the onset of the CY indication. Driver performance data from 53 participants were collected in the Oregon State University Driving Simulator, simulating scenarios of driving through high-speed intersections under various conditions. Data included interactions where the driver stopped at the stop line (n = 644) or proceeded through the intersection (n = 628) in response to a CY indication. Data were analyzed as panel data while considering 12 indicator variables related to the driver’s stop/go decision. These indicator variables included time to stop line (TTSL), tailway time, following vehicle type, vehicle speed at the onset of the CY indication, and demographics (age, gender, driving experience, level of education, personal vehicle type, number of times driving per week, number of miles driving last year, participation in previous simulation studies. A random-parameter binary logit model was used to determine contributing factors for driver decision making at the onset of CY indication while accounting for unobserved heterogeneity. Four indicator variables were significantly related to the driver’s stop/go decision, but three factors varied across observations. Findings showed that a driver’s stop/go decision in response to a CY indication was associated with the time to the stop line (TTSL), tailway time to the following vehicle, subject vehicle speed at the onset of the CY indication, and driver’s age (20–36 years), but was not significantly associated with classification of the following vehicle. Also, the findings indicated that a shorter tailway increased a subject driver’s red-light running frequency. These findings provide insights into variables that affect driver decisions in a vehicle-following situation at the onset of the CY indication. This information can help make better decisions in smart traffic control systems such as to extend/decrease the green interval slightly to avoid decisions that are more difficult.