Approximately where in the physical body does one feel a sense of soul?

It is in the spiritual heart. According to medical science, the heart is slightly to the left of the centre of the chest. According to Ramana Maharshi, the great sage of Arunachala, the spiritual heart is slightly to the right of centre. Some spiritual figures say that the heart is in the middle of the chest. But, according to one spiritual figure, the spiritual heart is located between the eyebrows! Of course, he also has his reasons for saying this.

The true spiritual heart, about four finger-breadths in width, is located approximately twelve finger-breadths directly above the navel and six finger-breadths directly below the centre of the throat. It is here that one feels what you have called the "quickening" of the soul.