Wasn't bibly who wrote about the immediacy of mind presence. Mind is in the moment is how I like to put it. Such a state cannot, IMHO, be an objective thing. What it is reporting can be objectively taken by another though. It is a state of brain processing which is center stage in one's consciousness theater. All three terms, mind, consciousness, theater, are broad constructions relating to states we hope have meaning to others rather than being real, material, things. A state in a process is no more than a relatively instantaneous reading or awareness reported or experienced. Treating it any other way leads to dualistic construction which is clearly not physically possible.
There is no way one can find a way to cement the mind into an objective thing because it is, at best, information, something communicated. What underlies the presentation is much more complex, rich, interconnected and continuing brain activity in line with evolved brain function.
Just as I can't tell you that what I see displayed on my oscilloscope arising from activity at a single cell is what that cell 'sees' at the Superior Olive is objective demonstration of SO function. We know what is recorded is resultant from input from the ear through the cochlear nucleus and resultant also from descending input to the inferior colliculus and probably the medial geniculate and auditory cortex. We know this because we record from and or all of these sites simultaneously. We've tracked such outputs from the earliest activity there to complete appreciation or stable perception of whatever is being presented being neurally represented at SO.
The Objective mind is only a place holder for what we know and understand as well as what we tell others we experience after we've experienced it.
You ask for something that does not exist except in what you say, It is never objective since what it is of which we are aware must always be reported as subjective since it is phenomenal rather than material and objective.
Philosophers and psychological clinicians and lay persons cannot even express what they 'know' objectively since what they know is often beyond what can be communicated and always subjective in nature.