Background: Computational thinking (CT) is an essential skill for preparing the younger generation to succeed in an AI-driven world, with pair programming emerging as a widely used approach to foster these skills. However, the role of individual factors and mutual engagement in shaping CT skills within pair programming remains underexplored, particularly in middle school contexts. Objectives: This study investigates how individuals' attitudes towards programming and collaboration, as well as individuals' prior computer and programming experience, influence CT skills in pair programming. Given the collaborative nature of pair programming, this research extends beyond individual outcomes to explore the mutual influence between partners, examining how these factors shape both individual and partner CT skills. Additionally, it evaluates mutual engagement as a moderator of these relationships. Methods: Eighty-four eighth-grade students participated in pair programming sessions using P5.js, a creative coding platform. Through the Actor-Partner Interdependence Model and dyadic data analysis, we evaluated the actor and partner effects of each individual factor and their interactions with mutual engagement. Results and Conclusions: Students' CT scores were positively associated with their attitudes towards programming and collaboration, but not with prior computer or programming experience. Their attitudes towards collaboration and programming frequency also positively influenced partners' CT performance. Mutual engagement moderates the actor effect of prior experience and the partner effect of social value (a subcomponent of attitudes towards programming) on CT performance. These findings enhance understanding of the social and cognitive dynamics in pair programming and provide actionable insights for designing activities that foster CT among young learners.