With the increasing consensus that a single effect of bilingualism is unlikely, some scholars shift their focus to elements that may exert an influence on the bilingual brain. One such element that has been garnering attention lately concerns the role of L1-L2 typological distance. In this conceptual analysis, I make the case that the foundations to commence this discussion are still weak at this juncture; conceptualisations of what qualifies as 'typologically similar' or 'distant' are not well-established in bilingualism research, and the tendency to compare languages as wholes, without considering dimensions and degrees of linguistic difference, can be problematic. Further, reflections on how bilingual cognitive demands are formed and how they are linked to L2 skill engagement (i.e. receptive/productive skills) are rudimentary yet underpowered. Crucially, I highlight the ongoing need to meticulously interpret bilingual neural activity and neurostructural changes before conclusions on the influence of typological distance can be reached. I conclude my critique by proposing a conceptual framework -- one that addresses language, cognition, and empirical methods in sequential order -- to help us embark more effectively on the theoretical inquiry of whether L1-L2 typological distance can pose an influence on the bilingual brain.