When the universe offers a sign — and the sign comes straight from the lips of Nicolas Cage — you can’t ignore it.

That, in essence, is how 31-year-old guitarist Ben Katzman found himself on Survivor. The paperwork sat on his desk, but Katzman was racked with doubt. He’d already lost everything once: his band, his record label, his DIY community. Going on reality television seemed like a potential career suicide. Which is where Cage comes in.

“Do the things you are fearful of,” the actor said, answering Katzman’s...