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I think Elvis' hair just grew that way from birth, I don't really know. It could be he used a really loose-toothed comb, and then the hair just drifted apart on the sides, weighted down with what my dad always called "greasy kid stuff."
for "Elvis hair" you want a large comb with both wide and narrow teeth, and some species of "flexible hold" gel or straight-up pomade product. "classic 50's pompadour" and/or "rockabilly pompadour" is what you are googling for tbh. This guy does a decent job at it, sans all the faffing about in the first 2 minutes or so getting the part / side lay clean - your hair is longer and finer and looks like it has a better taper so you shouldn't have as much trouble with that. What you're looking for is a sharp, clean part, and then the swoopy combing bit where you lay the crown into the peak of the "pompadour".
oh and, since you have some length on the sides, while you're going for a 'pomp, why not lay the sides back into a classic duck tail while you're at it? :)
(source: 80's goth punk product / hairstyling addict who revisited the '50s along with all her peers as a tween)