According to Mahayana abhidharma,
Mindfulness is a non-forgetfulness of the mind with respect to a familiar object. It has the function of non-distraction.
It is one the five object-ascertaining mental factors, and it is called 'object-ascertaining' because: > These mental factors hold [an object] through apprehending the > individual features of the object. They are said to "individually > ascertain objects."
As it is a mind, it is by nature clear and knowing, and it is a basis of designation of the person but is not the person. It is an apprehender, an object-possessor, but it is not a 'observer' because an observer is a person.
A mind, a cognizer such as mindfulness and so forth is possessed by a person (the agent), it has a function (the action) and apprehends its object.
There are various levels of nonduality. In general, a realization that occurs in a non-dualistic manner is free from the appearances of objects and subjects. So it is necessarily free from the apprehension of the object and the subject as being different substances.
In addition, mindfulness is not a process, it is a mind. As such:
- It has the nature of being clear
- It performs the function of knowing
That it is clear refers to the fact that it has the ability to take the aspect of its object. An eye-consciousness seeing blue takes the [subjective] aspect of blue.
That it is knowing refers to the fact that it apprehends its object. This point is quiet complicated and there is much debate. By nature a mind experiences its object. I hope this answer helps you, as you defined your "Observer" as an experience.