The main goal of this paper is to suggest a combination of data analyses -- notably generalized additive models, time-series clustering methodology, visual methods for significance testing and qualitative analyses -- that relate to Complex Dynamic Systems Theory (CDST). To this end, we report on findings from a larger project conducted in a bilingual (pre)primary school in Switzerland, aiming to elucidate the complex ways that L2 English development emerges over time in 45 children who received German/English bilingual instruction over a period of eight years (age 5-12) in combination with emerging extracurricular exposure to English. The results reveal that increased extracurricular activities in English are particularly noticeable during periods of rapid development, but the effects seem temporally limited to the end stages of testing and strongly hinge on the cluster in question (i.e., learners with trajectorial similarities). We relate the findings to the "authenticity gap" between English inside and outside of school, as clusters who perceive a discrepancy between in- and out-of-school encounters with English also show rapid development that is characterized by increased English exposure during extracurricular activities. Methodological implications of adopting non-linear models, which can model complex dynamic relationships in order to better reconcile generalizability, variability, and individuality, are discussed.