Sure, but here’s the thing, which colors all the conversations. When people think of Scotland and Scottish history…even when Scots think of Scotland and Scottish history, they think of the Highlands. You can maybe blame Sir Walter Scott for this, but probably not entirely. But, regardless, when somebody thinks of the archetypical Scot, they think of some Highland Laird, not of a barrister in Edinburgh. Even in Scottish Gaelic, the Lowlands is called * a’ Ghalldachd*…the home of the foreigner. A lot of it is tied up with the Jacobite rising, I think, and the way that, in the 19th century, Scottish nationalism and romantic sentiment tied itself to that…Culloden, Bonnie Prince Charlie and all that.
So, the Scottish Enlightenment took place in the 18th century, and people like Adam Smith, James Boswell, Hugh Blair, David Hume, John Leslie, Colin Maclaurin, etc, did shape the UK and, in fact, the world, but people don’t think of those people and that movement when they think of Scotland.
I’d disagree with you, though, when you say that the Second Jacobite Rising was “a foreign invasion.” It was obviously an invasion of England, certainly, but, while there was a plan to land French troops in 1743 to back Charles, a storm destroyed the invasion fleet. There were about 700 Irish troops fighting on the Jacobite side in '45, but the Jacobite forces were almost entirely Scottish (both Highlander and Lowlander…Edinburgh came out pretty strongly for Charles.)
For that matter, the same was true of the 1715 uprising. The Jacobite forces were primarily Scottish, with English (the Earl of Derwentwater) and Irish (the Irish Brigade) contingents,
Some people think that all Americans are John Wayne wannabes or that all Canadians speak French and live in igloos, but that doesn’t make a lick of difference to people who live there.