In a few places in Paul's letters, he speaks about imitating him or imitating Christ (1 Corinthians 4 and 11 also in Philippians 3). In my translations the invitation is to imitate not to mimic. I raise this for consideration because at least one distinction between imitating and mimicking is the direction of trust. Here is what I mean.
My sons are four and nine years old and they will, as children are prone to do, mimic my behavior. They parrot my words and mirror my actions. They trust that by mimicking me they are learning the things needed to survive and do well. Likewise, Christians trust Jesus and mimic him. Jesus shows us how to live and in mimicking him we grow and learn.
The direction of trust when we mimic flows from the student to the teacher. This is flow is inverted when we imitate.
As my sons grow older, it is my hope that they would slow their mimicking and increase their imitating. This movement requires that I as their father trust them to act in ways that I would hope they would act. I will not be able to control their actions or be present in every situation for them to know how to mimic. I have to trust my sons in order for them to imitate me. I have to give them freedom of choice and the possibility of failing or, even experience pain.
Likewise, Jesus is no longer physically present walking with each of us. We are not able to mimic him when it comes to contemporary problems and issues. How do we mimic Jesus in the face of the climate crisis? How would we mimic Jesus in knowing the ethicacy in the science of genetics?
Those who trust Jesus, over time begin to see that Jesus trusts us. Jesus does not desire us to stay at the mimic stage (all be it an important stage). Jesus desires us to mimic him so that we can move to imitating him. We will mess up. We will feel pain and suffering. We will miss the mark and participate in sin. The Good News is in part the reality that as imitators of Christ we are forgiven and trusted.
It is safe to mimic Christ. It is faithful to imitate Christ. Asking "what would Jesus do?" is a question for mimicking. Asking "what is Jesus trusting me to do/be?" is a question for imitators.