I think it's:
The palate
My reasoning:
Application of the mind is where I begin
Depictions of what is, what was, will be, and perhaps have never been
Palate can refer to someone's tastes, opinions, thoughts, etc. regarding appreciation of aesthetics.
Vibrant color with each illustrious stroke one will strive
Unlimited potential for an imagination that is now alive
A palate is what an artist uses to hold and mix different colors of paint while painting.
In the middle there is only me, this you knew
My neighbors make up two thirds of you
The palate is the middle, top part of your mouth. "Neighbors" could refer to teeth and tongue (bone and muscle, two thirds of the components of the mouth, with the remainder being soft tissue such as gums and palate) or to nose and mouth (both adjacent to the palate, and two of the three facial cavities, the third being the eyes).
As we come to the end we reach an uncomfortable state
Perhaps because of something off your plate
Gagging, heaving, flailing violently in attempts to mitigate
Always remember how essential it is to masticate
If you don't chew properly, food can get lodged in your palate and you can choke to death.