Thank you for your question. Wilayat al-faqih has two meanings. A jurisprudential meaning and a political meaning. The jurisprudential meaning of the guardianship of the jurist in the absence of the Imam is a result of the necessity of carrying out some jurisprudential laws which are specific to the Imam (as). The scope of this guardianship is discussed further on the books of fiqh.
Wilayt al-faqih as a political ideology for the period of the ghayba, was conceived by Ayatullah Khumayni (r) as a solution to the political vacuum that would be created after the overthrow of the Shah in Iran. While an autocracy had obvious flaws, there was much discussion on the role of democracy and its suitability as an Islamic system of government. In this milieu Ayatullah Khumayni proposed a system which drew from both the jurisprudential guardianship of a faqih, but also from his background in mysticism and the system of wilayat according to theoretical mysticism.
There is no definite system of governance that can be derived from the scriptural sources in the ghayba, and so different thinkers have had different ideas as to what that system should be like, and the conversation is dynamic in the contemporary Shia intellectual milieu.
May you always be successful