history is full of a lot of biases; arab sources push the primacy of arabs in the region, whereas more rigorous sources take into account what was very large scale migration from both germans and jews. but, this actually all happened rather late into history and doesn't really help us unravel the question, much.
i'm going to tell you such a thing doesn't really exist.
the first cities in spain were largely built by one of two peoples. the earliest semites in the region that we know of were the carthaginians, the ancestors of the modern day lebanese who got into a big war with the romans, who then took over the region as a consequence of winning that war. look up hannibal and the punic wars, if you don't know this history - which i find most people don't. if people knew the extent of carthaginian settlement in the region, they'd be less inclined to assign so much influence to the arab settlement, which was in truth both sporadic outside of a small number of settlements and actually mostly berber in composition. the arabs in spain were really recreating an ancient carthaginian maritime empire, by splitting it off from the former roman hegemony, almost in tact. so, the arab influence is generally over-emphasized in the arab sources. all of those j haplotypes aren't berber; it's more likely that they're carthaginian than arab, given that most of the major cities are carthaginian in origin, including cadiz, cartagena (new carthage) and tartessos. barcelona is also thought to be potentially of carthaginian origin.
the other colonies in spain and southern france that existed at the time of the punic wars were greek, although the only one that seems to have survived is the city of marseilles.
red is greek, yellow is phoenician and grey is latin. and, these are the earliest known settlements in the region.
but, if the earliest known settlements in the region are known colonies from people on the other side of the sea, and we can see the phenotypes of these early settlers in their descendants in the major cities of the south of the peninsula today, what did the people that lived there before the colonists moved in look like?
the people that lived there before the greeks and carthaginians moved in were celts, just like the celts in britain and france. they would have spoken a language that is not very similar to but in the same broad language group as gaelic - scots & irish. and, that's vaguely what they would have looked like. the historical record indicates physical characteristics such as red hair and green eyes all the way from spain to austria and beyond, on the northern and western edge of the roman domain.
these people traded with the greeks & phoenicians in a way that wasn't that different than the way that native americans later traded with the french and english - they would bring things like animal pelts or mined metals (including tin.) to the cities, which would be exchanged for more advanced technology, which they would take back to the wilderness with them. the world was bigger then, and they could coexist in that space, and did for quite some time.
but, we know that the celts are not indigenous to the region either, having migrated in from central europe and ultimately from eastern europe and central asia. who was there before the celts?
there were the beaker folk there before the celts, and we think they would have looked something like modern georgians or armenians, given the migration from northern turkey and the southern caucusus region with the spread of farming (even if there was some indo-european admixture by the time of the actual beaker folk, themselves). and, yes - there are megaliths like stonehenge all over spain, too.
but, they weren't indigenous either. and, we've exhausted meaningful history, and exhausted meaningful archaeology, too.
yet, there are still a people there that we believe predates even the beaker folk, and their neolithic ancestors.
the closest thing to indigenous people in spain are the basques, who are quite light-skinned but generally look a little more like armenians than they do like germans. it's really not known at all how they got there, or if they've always been there, but they must be a remnant of a very old population that survived in isolation in the mountains, much as various caucasian groups have survived in isolation in the caucasus mountains.
here's some basquey looking kids:
that said, there was also a substantive amount of gothic movement into spain near the end of the roman empire, and before the arab invasion. that lasted until 711, when they were defeated by arab forces. again: the arab sources present the situation as though there was an arab state in spain until 1492, but the truth is that it really only took a few decades before they were pushed out of the top part of the peninsula, leaving a series of coastal settlements that took centuries to slowly clean up. the carthaginians and berbers, together, left a much larger footprint.
as you can see, and i did something like this for italy earlier, at any point in time you're likely to get a mix of people in spain. in the historical record, we've always had a mix of semites, indo-europeans and north africans mixing together in this region, and so real world people would have been some kind of mix, pretty much throughout the entirety of history. the result is that spaniards throughout history would have tended towards a brown, even if it's a result of light & dark mixing, more or less perpetually.
but, the people that have been there the longest are the basques, and that's the closest thing to what we can call a native spaniard, at this time.