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
So are whites - it's really not going to make much of a difference. This is consideration #10 when it comes to evaluating your application. There are many other things that are more important when it comes to evaluating you, and as long as those things are up to snuff your race likely won't matter at all.