For many people, the phrase “Thanksgiving travel” means jammed airports and endless taillights. For those in the podcasting business, it means something else: a captive audience.

Even as the popularity of podcasts climbs, sparking recent moves by major players like Spotify and Google, consumers still struggle to discover new shows. Thanksgiving weekend, one of the heaviest travel periods of the year, offers the industry a key opportunity to reach those potential listeners.

This...