Well personally, I run into 3 kinds of people; (maybe 4 if you count those who believe election and have genuine faith).
1. Those who just lack the knowledge. And in my experience, these are generally people who for what ever reason just can't intellectually grasp it. In the cases of most of the people I know; it's a cognitive issue, an IQ issue, a developmental issue or an educational one.
Also in this category are people who may have psychiatric issues. What I tend to find with that group though is not generally an intellectual issue; but more in the category of personal self perception of being unworthy, useless, or that they would not be "lucky enough" to be elect. These people very well may acknowledge they know the doctrine is true. Their self perception though is of someone who's just unlovable. Which obviously takes a supernatural patience to break through that. Usually these people will improve quite dramatically psychologically; once their broken soul is healed. And in those cases, the change is usually quite dramatic.
In this "lack of knowledge category" though; it's usually obvious that it is literally lack of knowledge and not an issue with rebellion. Because these people generally don't argue with one over what they don't know, understand or "feel" about themselves related to Scripture. They'll puzzle over it, ask questions, or just flat out admit they either don't understand, or doubt this could apply to them based on their emotions.
But of course this doesn't mean that these types of people don't have genuine faith either. My son falls into this general category; as well as several other developmentally disabled people I've known over the years. Clearly some of them have (had - some of them have passed on now) genuine faith!
With the psychiatric population though; the complexities are usually a bit more compounded. And of course there are also the developmentally disabled who are "duel diagnosed".
My son fits much of this "lack of knowledge" category. He struggles emotionally with some traumatic things that have happened; but he also has some clear cognitive issues that prevent him from being able to put all the pieces of the puzzle together. He has memory and executive functioning issues that are a result of epilepsy. Which of course these deficits are obvious in other areas of his functioning too.
Over time though, people in these categories generally do gain more knowledge; as they become more grounded in faith. They just never would reach the capacity to give any sort of "theological dissertation" on the subject. (I.E. they can't explain what they know of how or why they believe to someone else.)
2. People who suddenly realize: O.M.G - that's actually in the Bible! These people are fun to have conversations with because one actually gets to witness their awakening. Usually from the recognition of "Yeah, that is actually there" comes the question of "Now what does it mean?" That's a process that can take time. And those who truly are awakened; never come to the point of full out rejecting it. They may genuinely scratch their heads over reconciling it against previous beliefs or what they'd been taught; but they aren't in rebellion against it either.
3. Those in rebellion. Most people I've encountered who reject election / doctrines of Grace are because of their own rebellion. In some of these cases; the doctrine of election is like a train coming down the track and they eventually come to a place where they "admit" election is correct. Sometimes they are honest enough to admit that they know it's correct and they don't like it. (Other times they "name it and claim it" thus fall into the "believer" category. Or at least in the sense of intellectual acquisition. Yet, admitting something is true is not the same thing as having faith!)
But more often than not; people in the rebellion category try to find ways around the doctrine and argue against election / doctrines of grace / "reformed theology". In these cases; I've found that most often it's not that the person lacks knowledge of Scripture. It's not a problem of cognition, intellect or education. It's a problem of obedience!
