Nine Lives by William Dalrymple is the best single book for understanding the religious world that underlies Jodhpur's lanes and temples. One chapter follows a Rajasthani folk musician — a practitioner of the ancient singing tradition of the Manganiyar caste — across the desert. Dalrymple writes about living faith rather than heritage tourism, and the chapter will change what you hear in the street musicians outside Mehrangarh gate.
City of Djinns by the same author is nominally about Delhi but contains some of the finest writing in English about Mughal and Rajput culture, providing context for the world that Mehrangarh Fort was built to represent. The Last Mughal, also Dalrymple, covers the 1857 uprising and its aftermath and is essential reading for anyone interested in the Rajput relationship with Mughal India and with the British.
Desert Places by Robyn Davidson is the author's account of travelling across Rajasthan with Rabari nomads and their camel herds. It is a book about movement, landscape, and belonging. Davidson is honest and precise about the harshness of the desert and the complexity of being an outsider in it. If you are heading into the Thar beyond Jodhpur, this will recalibrate your sense of the place.