Rev. Alexander Davidson gave evidence at the Napier Commission's hearing in Obe [Leverburgh] on 31 May 1883. You can read his evidence by clicking on the link on his name. He is the Minister of the Free Church in Harris, and is aged 70 at the time of Lord Napier's visit to his parish.
In his evidence, Rev Davidson says he has been in Harris since 1848, so we can trace him on the census registers. In 1851, he turns up for the first time as a Free Church Probationer in Moy, Inverness-shire, the 38-year old son of William and Margaret Davidson, farmers at Fornbeg, near Moy. Alexander has a sister, Eliza, who is 8 years his senior and a brother, William, who is 10 years younger.
In 1861, Rev Davidson is in the Free Church Manse at Manish, in the Bays area of Harris. He has a young family, Malcom (6), John (2) and Janna Arah (1) with Margaret as a baby of 3 months. A number of domestic and farm helpers also appear at the Manse. A decade later, we find Catherine, Anne and Janet, as well as Alexander (jr) and Thomas Robert added to the family.
In 1881, two years before the Royal Commission came to call, we find that the enumerator, recording the census, was William Davidson, the Minister's son, otherwise employed as a draper. Younger siblings include John (22), a shepherd; scholars Alexander (12), Thomas R (10), Samuel R (7), George (6) and youngest daughter Elizabeth M (2). Christina Mclennan (27) is a general servant in the Free Church Manse, as is Mary Mcmillan (22).
The Minister appears in the census for the last time in 1891, a year before his death. Only his son John is then left at home, as is his youngest daughter Mary Elizabeth, aged 12 by then. Alexander Davidson passed away on 15 July 1892, aged 80, suffering from senile debility. He died only 9 days after his daughter Janet had got married to Tiree man Donald Tulloch Mackay, a Free Church Minister himself (with thanks to fellow researcher Direcleit).
Harris Free Church, based at Leverburgh, remains active to date, and has a website. The Manse at Manish is no longer in use as such. It was built in 1853, and is presently a listed building. A list of Free Church ministers during the 19th century in Harris is given in this post by Direcleit, who has a lot more information on the history of South Harris in his blog.