Cindy, The information concerning the Whiteboys is quite accurate for the 18th century and it continued on into the 19th century and even spread to the United States with the most notable being the Molly Maguires in the coal fields of Pennsylvania in the late 1800's. The Whiteboys were very active in many counties and rampaged against their oppressors although frequently the results seemed to be indiscriminate.
Secret societies like the Whiteboys were very active in the late 18th century in Mayo and actually fought alongside the United Irishmen and the French Troops in 1798 in what was known as the "Year of the French". That Irish and French routed the British from Killala Bay in Mayo to somewhere not far from Aughrim in Galway where they were forced to retreat from Lord Cornwallis' troops.
Afterwards the French were allowed to sail back to France but the Irish suffered severe reprisals as a great number were executed for "treason". Perhaps the Wakefields lads were involved with this event or a similar type event on one side or another. But what I still don't understand is that one was beheaded, one jailed for life and two others had to flee for their lives. This would be understandable if they fought on the Catholic side (a lot of Protestants did)otherwise I am at loss but I don't doubt for a minute that something significant happened.
A place to check is the newspapers of the period such as the Freeman's Journal in Ireland starting from 1763 and several British newspapers that go back to the 18th century.