When Adam Schoen first noticed he was losing his sense of taste, his wife, Claire, wasn’t too worried. She also wasn’t fazed shortly after when he started noticing his balance was off. She didn’t flinch when the ear, nose and throat specialist couldn’t find any fluid in Adam’s ear, or even when the neurologist ordered an MRI.

But in July 2018, when the MRI came back, everything changed. It showed a mass near the stem of Adam’s...