Generative Artificial Intelligence (AI) tools have become embedded in the everyday academic practice of undergraduate engineering students, yet most large language models remain optimised for standard English rather than the code-mixed, multilingual registers through which students in linguistically plural regions actually think and communicate. This study examines technology acceptance of vernacular and code-mixed AI interaction among 84 undergraduate engineering students enrolled in APJ Abdul Kalam Technological University (KTU)-affiliated institutions in Kasaragod district, Kerala, a region historically described as Saptha Bhasha Sangama Bhoomi, the confluence land of seven languages. Using a structured questionnaire grounded in the Technology Acceptance Model (Davis, 1989), the study measured Perceived Usefulness (PU), Perceived Ease of Use (PEOU), Output Accuracy, and Linguistic Inclusion across five research hypotheses. Findings indicate that students from regional-medium secondary schooling backgrounds report significantly higher vernacular or code-mixed AI prompting than English-medium peers, chi-square(3, N = 84) = 22.91, p < .001. Perceived Usefulness correlates strongly with Perceived Ease of Use, r = .64, p < .001. Students who habitually use vernacular or code-mixed prompts report significantly higher ease of use than strictly English prompters, t(82) = 2.01, p = .048. Perceived terminological distortion is positively associated with reported reliance on AI-translated academic content, r = .27, p = .012, and native speakers of the unscripted Tulu dialect report markedly higher AI comprehension failure than speakers of scripted regional languages, t(79) = 11.60, p < .001. The results support all five hypotheses and highlight a persistent linguistic-inclusion gap in generative AI systems used within multilingual engineering classrooms. Implications for dialect-aware AI design and inclusive digital pedagogy in polyglot regions such as Kasaragod are discussed.