The 'mystery object is, as Sir Bruin says, a brass case for holding wax vestas or friction matches. These were patented in 1827 by John Walker (not the Johnnie Walker who invented Scotch) but did not become really popular until the 1840s, when this vesta box was probably made (well, circa 1840 to 1860). It must be remembered that this was long before the invention of electric light, and this box was made to be kept in a familiar place with one match in the holder at the top, so that if a light were needed, the match could be found in the dark. The match would be then taken from its holder, the holder turned upside down, and a light struck on the serrated base of the box, shown in the photo below. Then a candle, or a laid fire, or the gas light, could be lit by from the match. It still works very well with Swan Vestas or any red topped match (but not safety matches). It is, as I said in one of the comments, a very well thought out piece of equipment).
P.s. Well done, Sir Bruin!