An index fossil is one that lets you date a stratum, since the conditions under which it was laid down may vary, making it otherwise hard to identify.
In historical movies set in the United States after the end of WWI, popular music and cars serve the same purpose. Other things (like radio newscasts, or a popular TV show in the background) might do the same, but their use usually requires some plot or character action. Music and cars are everywhere. Music has the additional benefit of generating a soundtrack which can be marketed for little additional cost.
I recently saw Me and Orson Welles, which has a fairly extensive playlist of music from around its date, 1937.
(Short review: okay movie, a bit obvious, great performance from Christian McKay as Welles, Zac Efron as Richard is is too pretty and is no way suitable to the adorable lit geek Gretta Adler, and James Tupper really does look like the young Joseph Cotten--but could we avoid the coming-of-age cliche of the beautiful and talented woman who dumps you for the connections offered by a powerful older man, despite your overall wonderfulness? Maybe she dumped you because you are an annoying dweeb. I'm saying this as a friend. That's why you wrote the book/movie/blog post to get back at her, right? Get over it.)
Anyway I seem to remember something about music and cars. Oh, of course, Manhattan 1937. The index fossil of index fossils is Benny Goodman's "Sing, Sing, Sing", so that is here, along with some other old standards. But it isn't as bad as a Woody Allen soundtrack, which all indicate Allen's abiding fear that if we hear a tune we can't instantly identify, we will go into convulsions, bad for ticket sales. For some reason, the one I liked best, was Jimmy Dorsey's (brother of Johnny and Latissimus) performance of "The Music Goes Round and Round", under the credits. Only tunes that are both 1) big pop hits, and 2) get listened to or revived later are suitable as musical index fossils.
As usual, the round-fendered cars are all gleaming and perfect, even the taxicabs. In real life these are owned and maintained by auto enthusiasts, who don't seem interested in keeping cars in a state of arrested decay, say, five years past their prime. And, also as usual, only cars from immediately prior to the movie year are visible. No surviving Model T delivery truck, held together with spit and baling wire, putts by in the background. I noticed this particularly in Hollywoodland, set across the 1950s, where every car is gleamingly perfect. Sure, it's LA, but the seedy detective playbed by not-quite-seedy-enough Adrien Brody has a beautiful car too.
Would we accept a period movie in which the cars range from nice new ones to miserable heaps from two decades before, and a sound track of miserable novelty songs and romantic ballads by people no one ever heard from again? Probably not: movies are about dreams, not reality. But it's interesting to note how close to reality different movies feel like getting.