I would say the motivation was the fundamental motivation for all sin, which is coveting. To be like God was serpent’s temptation (3:3).
The following may be relevant to your previous comment:
In committing ourselves to Christ we learn—with the help of the Bible, the practices he gave us, the community of the church, prayer and the Helper, the Holy Spirit—to resist sin and choose good. Having fallen—originally as a people in the Garden of Eden, and individually as we all of us do as we are growing up—we learn to varying degree what sin is and what some of its worldly consequences are by sinning; that is, through experience. There is a saying, “The master has made more mistakes than the amateur has even tried.” It is much easier for us to recognize something when we have experienced it, and much easier for us to avoid it when we can recognize it. The path the Fall has caused us to take is both easier and more difficult. It’s easier because our BEING sinful makes sin more concrete and thus more easily perceived. It’s more difficult because sinning gets us into difficult situations and separates us from God, our only source of help. I would say the difficulty of it far outweighs the easiness.
But the goal is not to know sin, but rather to know, be capable of and always choose good. I am a piano teacher. If my students listen to me, I will guide them to the skills and knowledge they need to eventually go whatever direction they wish in playing the piano. They do not have to make technical mistakes in order to develop good technique. They don’t have to play music badly in order to learn to play it well. Some listen, some don’t. However they come to it, though, eventually they have to be able to choose good technique and playing music well or they will create problems for themselves, ranging from physical injury to personal dissatisfaction and unpleasant responses from others to insurmountable obstacles to their ambitions. I would much rather they listen to me, but I know there is a good chance they won’t, so I am prepared to use their disobedience for their benefit, seeking to help them learn from their bad choices. The benefit in that route, which is the route I took, is that they will be better able to teach, if they go that route, than if they’d always listened to me.
So my guess is that regardless of which path Adam and Eve took, the Tree of the Knowledge of Good and Evil and the serpent both had to be put in the garden that they might know they exist and have to choose either to trust or to disobey God. If they trusted God, they would know they exist but obey him regarding them. Then God could lead them to maturity—to knowing Good and Evil as did God and Jesus and the Holy Spirit—without having to experience sin through sinning.
We have Jesus as an example of someone like that. He became human, but he never sinned. He knew what sin and evil were, but did not have to learn that through sinning. He was fully mature, giving us a model for what that looks like.
Consequently, I would rather agree that we had to eat of that tree and fall, but that this is not because it is what God wanted us to do, but because of something inherent in us. And I think the evidence that it is not what he wanted is that he put both trees there and told us not to eat of the Tree of the Knowledge of Good and Evil. That first sin was, specifically, doing the opposite of what he’d said he wanted us to do.