I wanted to give an update, not only for everyone who gave advice but also for anyone who might come across this in a search.
Today I caught the male swimming normally and then diving to the bottom of the tank to lay on his side and play dead so I finally know what caused it. It was a reaction to being startled.
He was swimming normally in front of me while I was running some tests on the second quarantine tank. Without thinking, I started shaking the test tube in front of the tank. He immediately darted to the bottom, collapsed on his side, and froze in place.
I now realize that every time I was already in the room for a period of time, he didn't do it. However, there were a few occasions where I walked in to find him on the tank floor. I didn’t have any lighting over the tank, so I am fairly certain that turning on the light in the room elicited the startle response from him. It also explains why I never saw the female do it if it was some sort of toxin/medication reaction in the tank.
I put a light over the tank the day I made the last post in this thread, and until today, I had not seen the behavior again.