Public engagement is an important component of the operation of many physics organizations, such as physics departments. However, comparatively little work has been done to systematize the study of pedagogical approaches in these informal environments, which may contain unique affordances and challenges compared to formal settings. A 2016 study took an important step toward a comprehensive understanding of pedagogy in informal environments by developing a model articulating three so-called "modes of pedagogy," utilizing cultural-historical activity theory to categorize pedagogy of volunteer instructors. To build upon this model, we have conducted a more thorough study at a University of Colorado Boulder-based informal physics education program, following similar methods but expanding upon the methodology to generate more robust insights into instructors' pedagogy. The study has produced three major results. First, we have broadly corroborated the findings of the 2016 study, observing similar distributions of enacted pedagogical preferences among our volunteer instructors. Second, we have expanded upon recommendations in the 2016 study for methods of instructor preparation; specifically, we find that presemester training is insufficient to effect a lasting change in instructors' enacted pedagogy. Third, we have refined the pedagogical modes model presented in that work, moving away from a categorical articulation of the modes in favor of a model where instructors' pedagogy is characterized by combinations of traits and mediated by their overarching objectives for students. These two novel additions to the pedagogical modes framework allow for a more nuanced and comprehensive characterization of the pedagogical techniques used by instructors in informal learning environments, improving both our understanding of the methods of informal pedagogy and our ability to prepare instructors to succeed.