Jon Voight keeps moving. The 85-year-old actor is shadowboxing, his footwork nimble for a man of any age, let alone someone older than even Joe Biden and Voight’s friend Donald Trump.

He pauses and arches an eyebrow and becomes a matinee villain. “You think you’re tough. I’ll show you tough.”

Today, we’re outside his Beverly Hills home. There’s a pool and a driveway where Voight designed the pavement that features tiny ducklings, rabbits, monkeys and a dragon etched into the cement. Near the entrance are the words “Wots Modder Wot You Jonny,” in honor of his Czech grandfather who never quite mastered English.

I’ve talked with Voight many times over the past year, and he is always engaging. But the presence of a photographer has kicked him into a high gear. He picks up a plastic rabbit in his yard and speaks to it,...