Please give some reference from the scriptures mentioning that the soul is always active.

Here is the shloka no. 3.5 from Bhagavad-Gita As it is with complete translation and purport by His Divine A.C.Bhaktivedanta Swami Prabhupada.

na hi kascit ksanam api jatu tisthaty akarma-krt
karyate hy avasah karma sarvah prakrti-jair gunaih

TRANSLATION
Everyone is forced to act helplessly according to the qualities he has acquired from the modes of material nature; therefore no one can refrain from doing something, not even for a moment.

PURPORT
It is not a question of embodied life, but it is the nature of the soul to be always active. Without the presence of the spirit soul, the material body cannot move. The body is only a dead vehicle to be worked by the spirit soul, which is always active and cannot stop even for a moment. As such, the spirit soul has to be engaged in the good work of Krishna consciousness, otherwise it will be engaged in occupations dictated by illusory energy. In contact with material energy, the spirit soul acquires material modes, and to purify the soul from such affinities it is necessary to engage in the prescribed duties enjoined in the sastras. But if the soul is engaged in his natural function of Krishna consciousness, whatever he is able to do is good for him.