So for starters, here's a old answer of mine that addresses some of the ways that historians have dealt with miracles and the supernatural in the sources we study. It is Abrahamic, I'm afraid, but I'm on very shakey ground for anything outside Western Christianity, so that's the perspective I come at this question from.

Generally speaking, most historians subscribe (more or less) to the dictum of Brian Stock's that I quote in the above answer: 'the point is not whether the miracle “took place”, but that people whose social affiliations can be the object of empirical study explained their behaviour in terms of it.' The effect of this methodological approach is to effectively set the supernatural event per se (to borrow a phrasing from Goodich) outside the remit of the historian's judgement. We are interested in the social or cultural aspects that belief in such an event implies, or the cultural elements that lead to the interpretation and use of the supernatural event (either prior or subsequent to its actual occurence). So in your example, we don't need to consider whether the sun and storm gods helped Mursili II, we just need to consider what cultural factors might have built up a milieu where this was considered possible, or what claims Mursili (or the sources) are making about the event by evoking the gods in this manner.

However, I'm not entirely satisfied with this, and neither are some other historians. For me, I feel that the narrowing of the historian's scope to encompass only the behaviour of those in (cultural) proximity to the miracle/supernatural event has the unfortunate side-effect of eliminating questions of belief from the equation. Belief is a hugely important element of the mental worlds of our subjects, and to simply put it in a box and set it aside because 'we can't access it' is (in my view) to do a disservice to those we study. We need to take into account how belief 'worked', both in a social sense, but also in terms of how it impacted and provided the intellectual and cultural tools that people used to engage with their worlds. A (now slightly older) but still important article by Amy Hollywood takes up a similar cause, drawing on the work of Dipesh Chakrabarty, who works on South Asia and post-colonial history.

Chakrabarty has honestly taken a fairly radical stance on this issue, albeit one that I have a lot of sympathy towards. When considering how historians deal with claims of supernatural events, he points out that 'the historian, as historian[...] cannot invoke the supernatural in describing/explaining an event' - so, in your given example, we cannot accept that the gods help Mursili II in battle, because it simply isn't possible in our own epistemology. So far, so normal, and exactly as you've suggested in your post.

However, Chakrabarty (and thus Hollywood) then take the leap of arguing that the historian, to successfully write a history that doesn't subsume the alterity of the historical into the conceptual categories of the historians' own culture, must 'stay within the heterogenity of the moment' - i.e., accept the supernatural claims of their subjects, and allow them to provide an explanation for the events that are the object of study. There's a fine distinction here. Chakrabarty isn't making the simple (and obviously wrong) argument that in order to fully understand a supernatural occurence, you have to believe it. Neither is he making the patronising argument that we have to accept that they (our historical actors) believed in the event, but that we as a historian can remain detatched, as that really wouldn't be substantively different from Stock's argument above. Rather, Chakrabarty's point is that accepting the supernatural explanations for things forces us to acknowledge new 'ways of being', and the (complex) point that the present is noncontemporaneous with itself.

Furthermore, Chakrabarty seperates History into two strands, which he (groundbreakingly) calls History 1 and History 2. In this formulation, History 1 is the narrative that we impose on the events of the past (and the concepts and epistemology that implicitly underpin this narrative), whereas History 2 is what we might term the 'raw material', the actual messy and contradictory events (including supernatural ones) that form the data from which we fashion our narratives. He points out, basically, that History 1 is totally constructed, and that this is done according to Western liberal principles of 'how the world works' - i.e., secular, magic isn't real, religious (or supernatural) events always have some ulterior (if subconcious) function, etc. Hollywood takes this point, and from it suggests that in order to actually make sense of the sources we have that deal with supernatural events (whether that is Christian visionaries, Hittite gods, or anything in between), we have to acknowledge not only the belief of our historical subjects in these events, but the actual possibility of their reality, that the explanatory categories of our subjects have validity.

This is genuinely complex stuff, and it's something that I'm still working through in my own research. Indeed, there isn't necessarily a good answer. To dismiss supernatural explanations or events (or worse, try to explain them through 'modern science' - see Joan of Arc and ergot poisoning, or Catherine of Siena and anorexia) is patronising, hegemonising, and distorting. To sideline the supernatural in favour of the 'behaviour' it inspires is unsatisfying and incomplete. But to go 'full-Chakrabarty' and allow for the possibility of divine or supernatural intervention is incredibly difficult and complicated, as it (quite rightly) disrupts our comfortable epistemology, and threatens to throw us head-first into the worlds of our subjects, worlds that we are ill-equipped to deal with.

So to answer your question, at least to some extent: is it proper or improper for a historian to rule out as a matter of fact the miraculous and/or supernatural? Conventional historiography would side-step. Chakrabarty would say it's improper. Most historians simply don't consider it their problem, as it doesn't really impact the vast majority of historical work. I'd be inclined personally (as someone whose work it does impact) to side with Chakrabarty, but with some qualifications that I'm still in the process of working out.

I hope that helps - I appreciate it's a bit 'in process', but there genuinely isn't a simple (or even widely accepted) answer to the question you pose, and it's still a live issue in some historical fields, such as mine. Happy to try to answer any questions this may raise, as best I can.

Some Sources

Amy Hollywood, ‘Gender, Agency, and the Divine in Religious Historiography’, The Journal of Religion 84, No. 4 (2004): 514–28.

Dipesh Chakrabarty, Provincializing Europe: Postcolonial Thought and Historical Difference (Princeton, 2000; second edition, 2008)

Dipesh Chakrabarty, Habitations of Modernity: Essays in the Wake of Subaltern Studies (Chicago, 2002)

Bruno Latour, Rejoicing, Or the Torments of Religious Speech, (2002)

John Arnold, 'Believing in Belief: Gibbon, Latour, and the Social History of Religion', Past & Present 260 (2023 - forthcoming). There's a video of Arnold's lecture that forms the genesis of this article here, and it's well worth a watch.

"The Witch" by Ronald Hutton talks about this a bit, though it's not the primary topic of the book. He does make a clear case that when studying supernatural things (for the purposes of that book, witchcraft), historians need to be very careful to keep modern ideas of what is true or possible separate from what the accounts say.

For witches, and associated records (of trials, etc.) this means working through a lens that allows the accounts to be true to the people writing them, even if you as a 21st century reader don't believe them.

If we can more or less all agree that \something* happened and that the first followers believed they saw the risen Christ

From the folklorist's point of view, I see no convincing testimony about anything the first followers believed. One of the things that is truly shocking about oral tradition is how quickly the "oral" can become "tradition." Stories about a risen Christ were clearly circulating - and likely very quickly, but that does not mean that any of them were being spread by firsthand observers.

I understand that a great deal is invested into the idea that one or more of the Gospels were written by eyewitness observers of the events, but there is nothing I have seen that locks this in place without question.

On the other hand - again as a folklorist - I have encountered many first-person accounts of the remarkable, told in the form of "memorates" (a term coined by Carl Wilhelm von Sydow (1878-1952) for narratives/legends told in first person to be believed). People confront the world with their culture and belief system held close to the heart, and this has an effect on perception. That is a normal process, and to refer to people as "superstitious," for example, is only to demean the subjectivity that is part of the human condition.

All this means that for folklorists, we cannot begin by accepting the accounts as written without the understanding that people's perceptions of what happened is quickly affected by the way narratives are mutated in the telling.

None of this is to take away from the excellent answer by /u/GrumpyHistorian, whose response is excellent and is unaffected by anything written here.