Too bad CA dumped all their old historic records - not really but they require a hand search and they'll no longer do that. Or we could find the serial number from the yellow/black 1956 plate.
If the studio had 2 cars they would have painted a plate to put on the extra car. A hero car for all the closeup work and a stunt or backup car in case the hero didn't start. It's cheaper to have a second car than to pay the stars and crew to stand around while the prop guy tries to get one running. The first photo the plate looks flat and the closeup later photo it looks like the real embossed plate.
In that time period studios usually owned a fleet of cars to use or park in scenes. Today there are several companies that provide them.
This one is next to Leno's Garage.
https://www.google.com/maps/@34.2072...oASAFQAw%3D%3D