Listening to Dr Duncan  on Westminster theology now on the impassibility  of God. Genesis 6:5 to 6 says God recreated that he made men on the Earth and agreed him into his heart.

So in Westminster confession chapter 2 says God is spirit, and he doesn’t have a body. In Old Testament God uses anthropomorphic expression to describe eternal, spiritual God with our human and anatomy. So the impassibility  of God is that God is not controlled by things outside, all his impulses from within and consistent, invisible and incorporeal.

I find it hard to reconcile per se. But Carson’s. NIV study Bible says:

NIV Biblical Theology Study Bible Notes) 6:6 regretted. Does sin cause God to change his mind? Elsewhere the answer is no (Mal 3:6; Heb 6:17; Jas 1:17). Yet some passages suggest the opposite (1 Sam 15:11 [but see v. 29]; Jonah 3:10). God is involved personally with humanity. While his final purpose for humanity does not change, his means to carry that purpose forward may.

I find it very agreeable on the last sentence that purpose of God does not change, his means to carry the purpose forward, May. I think there’s exactly what happened to Genesis chapter 6. God changed his means achieving the purpose which has never changed. I guess the question is was he emotionally actually grieved? I would say that, even if he was grieved as scripture says, And as many scars as anthropomorphic expression, there is no contradiction because his purpose doesn’t change, his emotional response does not change his purpose, and therefore  he is still unchangeable, immutable, and therefore impassible. 

Jesus expressed his emotion frequently like he wept for Lazarus on his death with his sister, Mary and Mariam. I think it is incredibly important for God to feel our emotions and actually identify with us emotionally and not a detached stoic God that would’ve been like pantheism or Greek gods. 

Jesus cried out for the lost sheep of Israel that he longs to gather them as little chicks.

I guess the argument against that will be Jesus expressed his emotion as a man the incarnate God, but if we want to draw a connection to the emotional heartbeat of God, the only expression of that on earth will be the heart beat  of Christ walking on earth as he is also the perfect image of God. He is God. I will find it astonishing for God to incarnate into this world and expressed  his emotions,  scholars would explain that as an anthropomorphic expression of God. But Christ is also God walking on earth in a strange way. That dichotomy is therefore almost like a social construct to delineate it quite unnecessarily.

To argue for the unchangeability of God, the immutability of God, that is easy that even Gen 6 God was grieved and he regretted making mankind because they were evil sinners.  But he never changed because he is still a loving God and compassionate and a righteous holy God. His purpose never change. Is just a on the spot  manifestation of his emotion on individual cases that does not contradict impassibility  and immutability.

As for the sources of research, I will look into Augustine  in his confession , which is really a powerful book that book in itself consolidate humans emotions with God and in fact, it will be impossible for Augustine to write that on an emotionless God.  Augustine will never agree with the God that does not grieve inside or rejoice over us. 

Other sources like the Institute by John Calvin and some patristic literature and the historical theology I’m sure.

So my conclusion, the incarnate God came as a man to express the heartbeat of God, and if we take that away, defeats part of this incarnation expression or manifestation of his majesty, and the reality of who God is.