The Trails Restaurant (also known as The Trails or Trails Restaurant & Organ Bar), a Western-themed steakhouse/roadhouse on Route 66 (Huntington Drive) in Duarte, CA.
This iconic neon cowboy-on-bucking-horse sign (sometimes called the "Neon Cowboy Sign" or "Bucking Horse Sign") was a landmark for the restaurant, which operated from around 1952 until the early 2000s (demolished ~2001). It was photographed there in the 1970s by artist Jim Dow and matches the black-and-white image you shared exactly—showing the profiled cowboy in a hat riding the rearing horse, outlined in neon tubing.
The sign was saved after demolition, stored at the Duarte City Yard, and has been (or is being) restored for display, including at the California Route 66 Museum in Victorville.
This fits the 1960s timeframe perfectly, as it was a classic Route 66 stop with that distinctive Western neon signage.
