The growing number of people with cognitive impairment will significantly increase healthcare demand. Screening tools are crucial for detecting cognitive impairment due to a shortage of mental health experts aiming to improve the quality of life for those living with this condition. Eye tracking is a powerful tool that can provide deeper insights into human behavior and inner cognitive processes. The proposed Eye-Tracking-Based Trail-Making Test, ETMT, is a screening tool for monitoring a person’s cognitive function. The proposed system utilizes a fuzzy-inference system as an integral part of its framework to calculate comprehensive scores assessing visual search speed and focused attention. By employing an adaptive neuro-fuzzy-inference system, the tool provides an overall cognitive-impairment score, allowing psychologists to assess and quantify the extent of cognitive decline or impairment in their patients. The ETMT model offers a comprehensive understanding of cognitive abilities and identifies potential deficits in various domains. The results indicate that the ETMT model is a potential tool for evaluating cognitive impairment and can capture significant changes in eye movement behavior associated with cognitive impairment. It provides a convenient and affordable diagnosis, prioritizing healthcare resources for severe conditions while enhancing feedback to practitioners.