http://freepages.genealogy.rootsweb.com/~kayhin/61566.html- here he is in context, right? Thomas Wright, 33, gunner, C.B.R.A
Address is Pendennis Castle, and the head of household is listed as Lieut (C. B. Royal Artillery). C Battery maybe? (Someone who knows more about the RA should probably answer this one.

)
At any rate, I would suggest that he's in the RA at this point, clearly some time between 1861 and 1871 he left and joined up with the Militia.
Was his full name Thomas Burslem Wright?
The Times, Tuesday, Mar 07, 1876; pg. 9; Issue 28570; col F
- her Majesty the Queen held a Levee at Buckingham Palace yesterday afternoon.
(list of other royals, those guarding and attending upon the queen)
(description of the dress of the Queen and Princess Beatrice)
(lists of those attending the diplomatic circle, being mostly various ambassadors or ministers)
(lists of those in the general circle, being government officials or in impressive sounding military posts like 'First Naval Lord of the Admirality')
Then follows a list of those presented to the Queen, which include:
Captain T. Burslem Wright, Royal East Middlesex Militia, by Major Dyson-Laurie, 34th regiment.
(and followed by the names of others present).