The flappers wore a particular fashion, but it's naive to think that 'petting' happened in one moment in time. Records from the (actual) Puritans showed they were as sexually liberated as modern folks, albeit more concerned about how to raise any unexpected offspring (there was normally some deal in place for financial provision, if not marriage).

Kisses and foreplay at house parties and drive-in movies is a plot point in everything from Grease to Mean Girls, so 'petting' certainly didn't end with the flappers.

If it entered any kind of hiatus during WWII, it's only because people were outright having sex. If young ladies in the 50s were chaste in their teens and 20s, then all those babies-out-of-wedlock must have emerged from thin air.

The only things that seem to have changed in recent history are the words we use and the extent to which we lie about it.