White-tailed lizards can be found scattered about the Forbidden Lands in Shadow of the Colossus. One can be found at each save shrine, while many others can be found in the wild around certain locations. When Wander kills one, he can consume its tail for a stamina boost.
The white-tailed lizards are not to be confused with the regular fully black lizards, whose tails only replenish a small portion of Wander's health and do not raise either max health or max stamina. A Lizard Detection Stone can be unlocked by defeating 8 colossi in Normal Time Attack, or 10 in Hard. Their agility make them difficult targets, but it's good for getting in some practice with the bow.
If the lizard's tail is shot, the lizard can break free from its tail and survive, though this requires an extremely precise shot and more than a bit of luck. However, the lizard will still show up on the Lizard Detection Stone. Only by killing it, will the lizard's icon vanish.
Many species of lizards in real life can indeed detach their tails, a method typically used to trick their predators. The detached tail will even continue to wiggle around for a short while to further the illusion, and the lizard will grow a new tail in a matter of weeks. This process is called autotomy, and is not at all exclusive to lizards - spiders, crabs, lobsters and even octopuses are known to sever and regrow their own body parts.