In this song, the singer is fixated on a seductive woman who lives there. Could this woman be the Canadian singer Alannah Myles, famous for the song "Black Velvet
"? In a 1993 interview with Network
magazine, Plant gave a non-denial denial, saying: "We did tour together. We're good friends. I think the world of her. She's a great, powerful lady. She has one of the finest voices of the idiom. She was always very kind to me, very warm-hearted. But the road is the road. Forget about all the rumors, everything is true and untrue. '29 Palms' was written on tour, the last time we were in California."
Considering the lyrics, "It comes kinda hard when I hear your voice on the radio/ Taking me back down the road that leads back to you," Myles must be considered the prime suspect. Also note the line "her velvet glove."