Tome on the Phoenix in Death's Gambit is a Collectible. Collectibles in Death's Gambit are items that have its effects activate as soon as the item as found.
Their two hearts beat separately, the Phoenix acting as a host while sustaining the parasite with its infinite energy."
Tome on the Phoenix Location
Near the border area of the Central Sanctuary going to the Boss room of the Soul of the Phoenix and towards the Oblivion Vale. There would be a tower defended by an enemy with a kite shield. In order to get there, you would have to go through the platforms defended by crossbow enemies. After defeating the enemy, at the end of the hallway of the tower would be the tome.
Tome on the Phoenix Notes & Tips