They were raised in 1793 at Westport as the South Mayo Militia, and re-designated as Rifles in 1855, until they became the 3rd Battalion of the Connaught Rangers 31st July 1881.
Your GGF would have been on the permanent staff. The lower ranks would have enlisted for six years, and after 6-7 weeks of initial training, they would have turned out once a year for 6-8 weeks, during which time they would have been paid as Regulars. They could serve anywhere in the UK. Men who failed out turn out could be sent to prison. Three months with hard labour for missing two calls out was common.
Quartermasters were very important to the Militia, as the uniforms, rifles and other equipment was stored between callouts, so your GGGF would have been responsible for keeping them secure, and making sure that any repairs etc were carried out, until they were needed again.
His appointment should be recorded in the London Gazette -
www.london-gazette.co.uk You should search for South Mayo Militia as well as South Mayo Rifles as it often took years for chances to take effect. Similarly after 1881.
His records may be in WO97 in Kew. Lower ranks in the Militia are in WO96. If you cannot get to Kew Findmypast will publish both series by 2011. His Commissariat Staff Corps service should be in the Musters Books (WO12), while Militia musters are in WO13. You will have to visit Kew to research the Musters.
Before about 1873 the Militia came under the Lord Lieutenant of the county rather than the War Office, so early records may be in the county record office, or in private hands, or have been lost.
http://www.nationalarchives.gov.uk/catalogue/RdLeaflet.asp?sLeafletID=26If you post his name, age and the date of the information, we may be able to provide more
Ken