In late November 2016, I was enjoying Thanksgiving break in my hometown on the Columbia River in Washington state when I received an unexpected call from Vice President-elect Mike Pence. Would I meet with President-elect Donald Trump to discuss the job of secretary of defense?

I had taken no part in the election campaign and had never met or spoken to Mr. Trump, so to say that I was surprised is an understatement. Further, I knew that, absent a congressional waiver, federal law prohibited a former military officer from serving...