Striving seekers perceive the supreme Reality as abiding in their own within. However, those who lack purity as well as discrimination fail to perceive the same, even if they strive hard.
The presence of the Soul in the body is not a matter of doubt. Krishna had explained it right from the 2nd chapter (2.12). The discussion thereafter is based upon this fundamental fact. And staunch seekers do realize the Self in them without any difficulty, as they are able to think about the matter very clearly and wholesomely.
Yet many, nay most, fail to realize the Self, as they lack the requisite degree of purity of mind and discrimination of intelligence (viveka). Seeking the Self is not just an intellectual pursuit at all. The impetus is to be provided by the mind and heart.
Only when seekers have the required measure of inner purity and austerity, will their wish and resolve grace their effort. As Krishna stated while discussing Sthita-prajna and Sthita-dhee (Ch 2), the seeker must be free of desire, ego and possessiveness, which are the main hindrances to realize the Self. Purity implies extinction of these three.