This mixed-methods case study investigates learner engagement during pair work, focusing on four key aspects--behavioral, cognitive, emotional, and social engagement--and how these relate to task performance. The study included 60 university students (34 females, 26 males) learning English as a second language, who collaborated in pairs on a 20-minute writing task based on a four-panel comic strip. Data collection incorporated both quantitative and qualitative measures: behavioral engagement was assessed by counting words and turns in oral interactions; cognitive engagement by tallying Language-Related Episodes (LREs); emotional engagement through a post-task questionnaire; and social engagement by qualitatively analyzing pair interaction patterns. The data was first analyzed descriptively at five-minute intervals, followed by correlation analysis to explore relationships between engagement aspects. Cluster analysis was used to group participants with similar engagement profiles, and qualitative analysis provided a deeper look into pair interactions. The study reveals how engagement changes over time, the interrelations between different aspects of engagement, and how combinations of engagement dimensions influence pair work performance. It also highlights practical and methodological challenges, including managing task duration, capturing nuanced aspects of engagement, and understanding pair dynamics. Readers will gain insights into how a mixed-methods approach can comprehensively assess learner engagement, integrating both quantitative and qualitative measures, and how this can inform teaching practices and research in second language acquisition. [This content is provided in the format of an e-book.]