We discuss the benefits of incorporating into the study of bilingual production errors and their traditionally documented timing signatures (e.g., event-related potentials) certain types of oscillatory signatures, which can offer new implementational-level constraints for theories of bilingualism. We argue that a recent neural model of language, ROSE, can offer a neurocomputational account of syntactic transfer in bilingual production, capturing some of its formal properties and the scope of morphosyntactic sequencing failure modes. We take as a case study cross-linguistic influence (CLI) and attendant theories of functional inhibition/competition, and present these as being driven by specific oscillatory failure modes during L2 sentence planning. We argue that modeling CLI in this way not only offers the kind of linking hypothesis ROSE was built to encourage, but also licenses the exploration of more spatiotemporally complex biomarkers of language dysfunction than more commonly discussed neural signatures.