A Comparative Grammar of the Dravidian or South-Indian Family of Languages by Robert Caldwell is the foundational work of comparative Dravidian linguistics, written by the long-serving Anglican bishop of Tirunelveli and published in 1856. Long, dense, and astonishingly modern in its method; the only book of its time to put Tamil, Telugu, Kannada, and Malayalam on a firm scientific footing.
The Hungry Tide of History by V. Ramachandran is a recent local history of the Thamirabarani valley from prehistoric times to the present, weaving together archaeology, temple inscriptions, and oral tradition. Best read after a visit to the Porunai Museum.
My God Died Young by Sasthi Brata — although not specifically about Tirunelveli — is one of the most candid memoirs of growing up in a south Indian Brahmin family in the colonial period, and gives a vivid sense of what mission-college towns like Palayamkottai were like in the early 20th century.
For broader Tamil context, Vikram Sampath's Splendours of Royal Mysore and A.R. Venkatachalapathy's The Province of the Book are both useful, even though their main focus lies further north.