I wrote a Masters' thesis on almost this exact question, the second part of your inquiry at least. It is correct that, as a part of the United Kingdom since 1707, Scotland did not plan an independent role in the war.

However, Scottish attitudes toward the Union were ambivalent at the time. Many still felt like a distinct nation and felt themselves as removed from the centers of power as the Americans (of course they had representation in Parliament, but didn't feel like they had the political influence they deserved).

On the other hand, a good many Scots were interested in the economic advantages to be gained from union and access to the English, now British, colonies and were perfectly at ease within the Empire. The famous enlightenment philosopher David Hume preferred the term "North Britain," as others did, as an acknowledgement that Scotland as a political entity had been absorbed by the new British identity.

The American Crisis, as the period during American protests but before war broke out was known in the UK, was also only about 20 years or so removed from the '45, the Jacobite Uprising wherein Bonnie Prince Charlie led an army of Highlanders to restore the Stuart dynasty to the Scottish and English thrones. Many Highlanders fled to America in the wake of the crushing defeat of the rebellion, mostly to the southern backcountry and the clan system combined with animosity against Britain led to some savage fighting among settlers in the area. Partially as a legacy of the '45, during the war, Parliament refused to grant Scotland the right to form defensive militias, despite allowing the Irish to do the same, and despite John Paul Jones' raids of his homelands around Glasgow and the threat of repeated attacks on Scotland once France entered the war. Many Scots saw this as a profound insult to refuse them the right to defend themselves.

Needless to say, Scotland's relationship with Parliament and the union in general was rocky. Therefore, during the Crisis and even the early part of the war, there was a vigorous debate over the merits of American complaints. An Edinburgh debating society had exactly that as the topic of one of their regular meetings, Francis Hutchinson wrote a pamphlet asking "when it is that colonies may become independent," and Adam Smith devised a new imperial order in which Parliament would cede many of its powers to America as a somewhat separate entity within the empire to preserve the commercial ties. There was also vigorous debate on the quality of the ministry at the time, questioning their policies and inquiring about corruption or incompetence.

This type of curious inquiry into the merit and nature of the Constitutional issues the Americans raised faded as the war deepened and stopped almost entirely once the French openly entered the war in 1778. The French were formerly allies to the Scottish against the English, but after 1707, Scotland had adopted the rivalry with France and were more interested in survival and martial success for the empire against a powerful foe.

My thesis has not yet been published, so I will save you the trouble of recommending it to you, but I would recommend some others. "Scotland, Europe, and the American Revolution", edited by George Shepperson and Owen Dudley Edwards, is the result of a conference on the same topic "Britons" by Linda Colley which looks closely at the rivalry with France as a catalyst for creating a British identity. "Scotland and America" edited by Richard Sher and Jeffrey Smitten is a collection of essays that deal with connections between the two entities in the 18th century. Eliga Gould's "Persistence of Empire" also looks at how the American War of Independence was perceived in Britain and changed attitudes toward governing the empire.