Around the 1950s and 1960s there was a lot of work in particle physics motivated by two issues - finding a workable quantum field model for the weak interaction, and finding a model that unified the weak and electromagnetic interactions.
I can easily see why the former was of interest (EM had a classical field explanation since Maxwell, and QED was a recent and stunning success, so the implication that a quantum field theory model would exist for the weak and EM interactions was clear).
But why was there any belief or expectation (beyond "elegance" and mysticism) to believe that EM and W were the two facets of a single unified interaction? (Other than in the broadest sense that everything is a facet of some grand theory of everything: this seems much more specific).
After all, the only unified interactions at that point were electricity and magnetism, both of which could be observed directly to create effects of the other type, and had been unified long ago. But as far as I'm aware there was no "smoking gun" that did the same and made clear that these were two sides of a unified "electroweak" whole, and at that point no other forces had been unified to suggest this was common. If anything, practical unification dreams had failed - gravity hadn't been reconciled even with QM, let alone with any of the 3 known other forces.
So what led people to such a belief that the 60's gave rise to multiple theoreticians who judged their theories based on whether unification 'worked', or who used that as a guide or outcome?