The vigilance of surgeons while operating is an important consideration for patient safety. Using a lightweight mobile eyegaze tracker, we can objectively observe and quantify a surgeon's vigilance measured as the frequency and duration of time spent gazing at an anaesthesia monitor displaying various patient vital signs. Expert surgeons and training surgical residents had their eyegaze recorded while performing a mock partial cholecystectomy on a computer simulator. Results show that experts glanced at the patient vital signs more than the residents, indicating a higher level of surgical vigilance.