This quote from Andrew A Bonar isn’t a complete answer, but I’m posting it to set the stage for (hopefully, perhaps, maybe) writing something in my own words later … time permitting …
Resting on this Person [ie Christ, the Son of God in our nature] for salvation is called “faith in Jesus Christ.” In this faith, there is an intellectual act – namely, the apprehending of the meaning of what is stated concerning Jesus. But this apprehension of the meaning of what is stated, or testified, concerning Jesus, is but the avenue that leads on to the magnificent mansion. It leads the soul to the Person of whom these things are declared. It is never the belief of bare propositions that saves the soul; for these have only to do with the understanding. Propositions, however weighty, must guide us onward to the Person who is the essence of the testimony; and they are made use of for this end by the same Holy Spirit who enlightens our once carnal understanding to see the real truth. The belief of the testimony, or record, concerning the Son of God, our Saviour, is the porch of the building, through which we pass into the audience-chamber and meet the Living Inhabitant, full of light, and life, and love.
Throughout the book which contains this paragraph, Bonar draws from the writings of other pastors and theologians who made the same point. Some of them I haven’t heard of, but they were presumably well enough known to a nineteenth century Scottish minister like Bonar and his audience. In a footnote to this paragraph, someone called Sievewright is quoted as saying, “Faith is not so much a disposition of the mind toward the truth, as a disposition of the heart toward Christ, produced by means of the truth.”
Even if these excerpts don’t perhaps show precisely that trust is what’s necessary, they are both clearly trying to show that assent alone is not enough to constitute the kind of faith that is required by the gospel.
Andrew A Bonar, The Gospel Pointing to the Person of Christ, 1858. Quote from p3-4 of the edition republished 1988 by Christian Focus Publications, with the title, The Person of Christ.