Take all questions in stride
Over the course of my four separate pat-downs, I faced a bizarre range of questions, from the standard, “Where are you headed?” to the slightly stranger, “Where do you think you lost your license?” (Does it matter?) It honestly felt like the agents were just trying to get a feel for my general level of sanity (which they're trained to do as part of the behavioral detection program), which of course made me nervous, which was probably not the best vibe to be putting out there.
Some ID is better than no ID at all
If you’re gonna be the dolt who loses her license, the best-case scenario is to be a dolt with another form of picture ID. Sure, a Costco card isn’t government-issued, but the agent who conducts the additional security is going to ask for anything that proves you are who you say. Between my Visa and my ATM card, I was mostly able to appease the authorities, but a 10-year-old grad school ID probably would have carried a lot more weight.