In all manner of historical pieces (presented both by scholars and laymen), certain figures are referred to as "mythical" or "historical." Characters such as Ragnar Lothbrok, King Arthur, and Emperor Jimmu are usually referred to as such, and which stories about them are factual (and in some cases, if they existed at all) is often a point of debate.
I am interested in knowing what makes some figures widely accepted as having existed, while others are considered "legendary" or "mythical," with their existence disputed. I assume this is a matter of the amount, type, and contents of primary sources available on them. What kind of primary source is considered acceptable to lend weight to their existence and what amount or breadth of information is "enough" for a figure to become widely accepted as having existed?
I understand that on some level this is a matter of opinion of what each historian might consider sufficient to cause them to lean one way or the other, but I am hoping for some sense of what generally tips the scale. Thanks!
The difference between legendary and historical figures is somewhat vague, but the ideal evidence for the historical existence of a person or ruler would be the existence of contemporaneous textual source material directly related to that person. In practice, historians dial with a variety of texts and materials with varying degrees of credibility and usefulness, and often complex chains of evidence are constructed.
Let me illustrate this with the example of Gilgamesh, who is probably the earliest iconic legendary hero. Gilgamesh was the ruler of Uruk, now considered a "semi-legendary" or "possibly historical" individual who may have lived roughly in the 26th century BCE. Gilgamesh is mentioned in the Sumerian King List, which is an ancient scholarly composition that contains both mythological accounts (including antediluvian kings ruling thousands of years) as well as historical information that can be more or less verified from other ancient historical documents. In fact, these same sources probably also served as the source material for the scholars who composed the Sumerian King List probably in 18th century BCE. However, it is difficult to determine just which part of the King List are historical, as modern scholars don't have all the same material as the ancient ones, while the ancient scribes clearly misunderstood parts of their source material, to the effect that they place contemporaneous rulers to different eras. In any case, Gilgamesh in the King List is said to be the "son of a phantom" and to have ruled for 126 years, so that doesn't exactly help much.
The actual "Epic of Gilgamesh" was composed, partially based on earlier poems and (probably) oral narratives, first in the 18th century BCE; the so-called "Standard Babylonian" which is best attested and most well known today was composed sometime in the late 2nd millennium BCE. So by that time, over a thousand years had passed from the time when Gilgamesh may have lived; in terms of content, of course, the Epic is an adventure story with mythological and philosophical implications, with hardly any relevant historical information whatsoever. So that also doesn't help much.
The most compelling evidence that Gilgamesh was, in fact, a real person has to do with Enmebaragesi of Kish, the father of Aga of Kish, whom Gilgamesh fights a war with in in Gilgamesh and Aga, one of those earlier Sumerian poems. Enmebaragesi is also mentioned in the Sumerian King List where he rules for 900 years, so he was previously thought to be a largely mythical figure as well. But as it happens, his name is inscribed on several alabaster fragments, one of which was discovered in the Temple Oval of Khafajah, which dates to about 2700 BCE, which essentially proves that at least Enmebaragesi did in fact exist and rule Kish. While this does not directly prove that Gilgamesh existed, it makes it much more credible, as it makes it quite clear that the Sumerians scholars who composed the King List did in fact have source material dating all the way back to the 27th century, and could very well have had similar material of Gilgamesh as well.
The Kojiki, from which the account about Emperor Jimmu derives from, is in my admittedly limited understanding a source material that is quite similar to the Sumerian King List; it contains both mythological and historical information, but given its relatively late composition in comparison to the events and stories it describes, it is not by itself a credible source. To verify such stories it'd be necessary to find older material which could somehow corroborate them.