So, one of Einstein's insights was that the speed of light is constant in all reference frames. What was the basis for inferring that?

Like, sure, if you assume it to be true, it has great predictive power, lots of interesting things fall out of the math that were verified experimentally, all that shit, whatever. But, historically, what justified making that assumption? Why was that a sensible conclusion to reach? What pieces of evidence made us all say "ok yeah, actually, we're convinced the speed of light is constant"?