Tome on the Kaern 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.
It's unknown whether by chance or fate, the Amarogs discovered they could achieve immortality through ritual sacrifice. The green crystals are a byproduct of their ceremony."
Tome on the Kaern Location
From the entrance of the Oblivion Vale go left. Continue moving left eliminate as you go and then go down the hill then enter the cave. After entering the cave there would be a rest area and some traps ahead. In the middle of the traps would be a wooden platform from which the player can descend from. After descending you will find the tome.
Tome on the Kaern Notes & Tips