The Vaishnava says that when a new avatar comes, all older avatars have already receded to what is called the causal body. The latest avatar remains in the subtle body until the next embodiment as an avatar. When the avatar recedes further back into the causal body, it requires a lot of sadhana to access. Rama, Krishna, Jesus are all available, but a lot of the great saints of different mystical traditions don't want to go and meet them. So yes, the avatar is present across time. I mentioned that the avatar is a spiritual teacher, Adi Guru. That's why you will find in Vedanta in general, in Hinduism, guru