I have an ancestor who was transported from County Tyrone to Van Diemens Land in 1843 at the age of 23. He was rumoured to have been politically active at the time. As he was a young Catholic farm labourer, I figured he may have been part of the Ribbonmen, who were active in Northern Ireland at the time.
Can anyone provide any insights or suggested reading on County Tyrone around this time?
Agrarian unrest was alive and well in County Tyrone between the 1770s and early 1900s. The Hearts of Steel Boys were one of the earliest organizations to reach County Tyrone in particular in the 1770s (though they were generally Presbyterian rather than Catholic). Ribbonmen were definitely present in Tyrone in the mid and late-19th century. However, it is difficult to differentiate between the various societies because the British authorities often simply called them "Whiteboys" (the name of another agrarian society) or "Moonlighters" (late 19th century). This sometimes obscures the real differences between these organizations.
The initial unrest in many counties of what we now call Northern Ireland began mostly as the result of competition over land between different economic interests (for example, strong farmers versus small holders or cottiers versus farmers). Also, in the northern parts of the country, industrialization did cause some difficulties for farmers as well. All of this fits into a very rich tradition of agrarian unrest and secret societies. Despite the secret nature of these societies, Ireland seems to have had more secret agrarian societies than almost any other nation at this time. If your ancestor was a farmer, cottier, or laborer who got the short end of the stick, odds are decent that he joined one of the many agrarian societies in Ireland at this time. Finding out which one is actually quite difficult as they rarely maintained rosters- a good window into this mentality is this Ribbonmen oath put up for auction.
For basic background, I would suggest The Oxford Handbook of Modern Irish History which provides a pretty decent context for all of this over a few pages. The anthology Irish Peasants: Violence & Political Unrest, 1780-1914 gives some good general information on various agrarian movements. Perhaps one of the best anthologies on agrarian movements is Jim Smyth's The Men of No Property Irish Radicals and Popular Politics in the Late Eighteenth Century As far as County Tyrone itself goes, the major book on Ribbonism- Fenians and Ribbonmen: The Development of Republican Politics in East Tyrone, 1898–1918 - really covers a later period, but might have some useful background as well.