put yourself down as white, won't make a difference either way. not sure how you'd be "gaming" anything since neither race gets any sort of preferential treatment in terms of admissions so it'll basically be a wash
i doubt there is any secondary that will ask such questions, i definitely didn't see it. secondaries are designed to get to know your aspirations and personality more, though some are designed simply to collect some money from you. the place this might come up is in an interview but not as a way to interrogate you about your AMCAS race selection but as small talk