I could be egocentric, but I'm going with INFJ on this one. Repeatedly, David shows that he is Ni over Fe.
David was the only one who stood up to Goliath. An ENFJ would have been too consumed with their lack of having the social role to do so (Fe). An INFJ would do it if no one else would, even if it wasn't his place (Ni).
Also, a dominant Ni could have given him the talent to know when to let that stone go to hit Goliath right between the eyes. Ni can cause some extremely zen like results from people who have almost no experience with something, and even better from those who are practiced, and David used that sling to hunt. A dominant Fe in a situation highly charged with emotion would likely have missed by putting too much enthusiasm, fear, nerves, drive, etc. into the shot. Clearly, David had extremely strong Ni early in his life.
David did not actually mature that quickly. In fact, he didn't even want to be king because he understood the implications (Ni). He spent years and years hiding out in caves learning how to lead before he took the throne. This is evidence that David had to grow into his Feeling function, proving it to be secondary. If he were an ENFJ, he would have jumped into the more preferred social role (Fe).
INFJ: "You want me to be responsible for EVERYONE? Do you have any idea how heavy of a burden that would be? I am not capable of that."
ENFJ: "I'm King!? SWEET!"
David didn't have a 'silly switch' so much as a 'if I feel like God is telling me to do it, I will, no questions asked switch' (Ni). It didn't matter how ridiculous it was, he would do it. The best example was running around in his underpants yelling praises at God, knowing full well people were going to see him doing it (decidedly not Fe).
David wrote Psalm after Psalm. While songwriting is an artistic manifestation of Ni, Fe, Ti and Se, the content of his Psalms focus on what he is percieving in the world around him. "I see how they look at me." "I know their intentions even though they smile at me" (Ni). Ni is designed to seek harmony, which is why it automatically goes toward the simplest truth. David also wrote about what he wanted most, which was serenity "You calm my troubles, and lead me to still waters." If David was Fe dominant, his Psalms would focus much more on the fact that he enjoyed his role as King, or that others were not playing their roles as his subjects. David would regularly lower himself to servant like status for others, "I wore sackcloth and mourned for them" (not Fe). Only as David grew older did his wisdom (Fe) truly develop. Until then, he only had insight (Ni), though massive amounts of it, evidenced by being hyper aware of things but often asking "Why?"
Most importantly, David's primary focus in his entire life, as recorded by himself and those that wrote about him was his relationship with God as he felt it, whether it meant his death, ruin, embarrassment, exile, or anything else (you can't get any more Ni dominant than that). However, as King, he did take his role very seriously and cherished every one of his subjects to such a degree that when he wronged any of them, he felt massive amounts of guilt (Fe secondary to Ni).
David was also quite a sensualist, as opposed to a lecher. The weakness that caused him to make the majority of his mistakes was not lust but love. He wanted true love so desperately that when he thought he had a chance at it, he had one of his servants killed, even though he knew it was wrong and would cause a lot of problems (another example of an underdeveloped Fe).
Lastly, David was a fearsome combatant, proven over and over in long battles and one on one contests (Ni). As a life long martial artist who spars on a regular basis, I can attest to the fact that the most difficult people to beat in an actual fight are Ni or Se dominant people (which have Se or Ni respectively as their inferior or 'Anima' function, making this conscious and subconscious pair of functions profoundly potent). We have the ability to move reactively and reflexively to exactly where we need to while our opponents are tied up trying to think about what to do next. Again, this is that zenlike effect I mentioned. David's ability to come out on top of all of these battles could not have come from brawn alone, nor practiced skill. In the thick of battle, one only has time to react, and Ni is the best function for this, hands down. While an ENFJ has Ni, it is much less likely as a secondary function that it would have seen David through so many fights undefeated (Fe and Ti dominant and anima pairs would have made him 'think too much' in combat for such a record).
Granted, I believe that God was behind the vast majority of David's successes. But, if David was a human, then he likely had cognitive functions like the rest of us, and as an INFJ, he would have been much more inclined to 'hear God's voice' to do all of the wonderous things I've mentioned. With Fe as a secondary function, he would have been able to humble himself before his courts and his people, but would have the conscience to serve them to the best of his ability.
Yeah, David is ours.
