At least since the days of the Moral Majority, I'd say. (Or possibly since the House Un-American Activities Committee. (Or maybe since Industrial Revolution-era strike-breaking? (Or maybe - if you're gay, transgender, etc. - roughly since the Old Testament was penned?)))

In other words: IMHO, social conservatism is very much authoritarian, in that it seeks to proscribe certain modes of living as contrary to the moral fabric of society. Saudi Arabia is, in this view, a prime example of this as it approaches its logical extreme. Fiscal conservatism, OTOH, doesn't necessarily have anything to do with authoritarianism. We've unfortunately managed to conflate the two in modern American politics, which is how you end up with counter-productive policies like "tough on crime", "war on drugs", "cut basic social services", etc. that end up costing more than necessary in the service of "proving" a moral point.

Since at least the early 19th century? In Europe, conservatives were the ones who supported absolute monarchies.

Thats because absolute monarchies were the status quo in the 19th century (except for switzerland and france -- on and off). Conservatism is a political agenda to preserve the status quo. Going further back and revive concepts of a long forgotten past is usually called reactionary.

What is now the UK hasn't had anything like an absolute monarch since the 17th century - indeed you could argue that the last one got his head chopped off!