There have been several attempts to conceptualize and operationalize pedagogical content knowledge (PCK) in the context of teachers' professional competencies. A recent and popular model is the Refined Consensus Model (RCM), which proposes a framework of dispositional competencies (personal PCK--pPCK) that influence more action-related competencies (enacted PCK--ePCK) and vice versa. However, descriptions of the internal structure of pPCK and possible knowledge domains that might develop independently are still limited, being either primarily theoretically motivated or strictly hierarchical and therefore of limited use, for example, for formative feedback and further development of the RCM. Meanwhile, a non-hierarchical differentiation for the ePCK regarding the plan-teach-reflect cycle has emerged. In this study, we present an exploratory computational approach to investigate pre-service teachers' pPCK for a similar non-hierarchical structure using a large dataset of responses to a pPCK questionnaire (N=846). We drew on theoretical foundations and previous empirical findings to achieve interpretability by integrating this external knowledge into our analyses using the Computational Grounded Theory (CGT) framework. The results of a cluster analysis of the pPCK scores indicate the emergence of prototypical groups, which we refer to as competency profiles: (1) a group with low performance, (2) a group with relatively advanced competency in using pPCK to create instructional elements, (3) a group with relatively advanced competency in using pPCK to assess and analyze described instructional elements, and (4) a group with high performance. These groups show tendencies for certain language usage, which we analyze using a structural topic model in a CGT-inspired pattern refinement step. We verify these patterns by demonstrating the ability of a machine learning model to predict the competency profile assignments. Finally, we discuss some implications of the results for the further development of the RCM and their potential usability for an automated formative assessment.