The narrator and his buddy, Crewlaw, cruise out to Azusa where Crewlaw's dad burned to death in a fire started by his smoking in bed. Crewlaw uses the pretense that his friend doesn't believe him but Crewlaw probably needs to see for himself and/or for some sort of closure. We do not learn whether or not there had already been a funeral. The setting is very visual and immediate. It's told in first-person POV which assists in the sense of immediacy and reality.
"We drove out to Azusa on Highway 66 in Crewlaw's '48 Mercury with gray-primered skirts and parked on a gravel lot beside the Jupiter Motel, one of those quasi-Spanish-stucco courtyard jobs with a dead fountain in the middle and no customers."
For me, the theme is about living and how no matter the style of living you choose to do, it's living and also that no matter what you do, time passes and life happens and it ends.
"'What was he doing way out here?'
'Living. What do you think he was doing?'"
Later, Aunt Mellie said.
"'He's run flat out of tomorrows!'"
"'Believe you me. Things happen before you even know it.'"
Crewlaw insists on showing his friend, the narrator, the mattress his father died in. They find it and dump it into the Flood Control Aqueduct and set it on fire.
"'Now he's all the way gone.'"
At the bottom of the embankment, the mattress lands on an old washing machine. There's water and fire, baptism or cleansing and funeral pyre.
The title is reiterated in this line. "I had a definite sense of somehow being a passenger in an evil vehicle cruising through Paradise."
The story takes place in about 1957. Crewlaw's car is a '48 Mercury that already has already been primed. The movie Jailhouse Rock premiered in late 1957.
Shepard wrote the short story March 5, 1989 in Los Angeles. The collection Cruising Paradise: Tales was published in 1996.