To some people, there’s no one like Ed Maverick, the Mexican singer with a singular voice, able to share the deepest thoughts of his listeners through his unmistakable baritone. But ask Maverick himself and he just thinks of himself as a guy trying to make sense of his own feelings while keeping his music going.

“If I’m still alive and I’ve made the decision to keep on living — and there have been times when I didn’t want to be — I might as well push these ideas,...