It doesn't start in a 'cave' but this one sounds as close to your description from the top of my head;
http://thiefmissions.com/info.cgi?m=ShadowsOfEidolon
does anyone remembeer the mission in which garrett starts off in a cave ,he needs to find a flare, its all dark,there are haunts in it one appears when he reads a book,
It doesn't start in a 'cave' but this one sounds as close to your description from the top of my head;
http://thiefmissions.com/info.cgi?m=ShadowsOfEidolon
now i cant find the flare,