This is actually a wonderful question, even more so because of your application of the response in reenactment, which I find fascinating myself. I will hopefully do my very best to relay to you the most recent developments , understanding and conceptions of the cult itself, as well as avenues if information which will aid you in your future endevours of reenactment. Archaeology is our foremost applicable tool of extracting data in this regard, in formulating our current conceptions on the topic, as I am quite sure from what you have grasped already, very little, if any at all remains in the vein of primary source evidence. So with this potent tool of history research art our disposal we shall delve into the wonderful world of excavation reports. I will o my best to extract some interesting data from the most recent reports published and available to us at this time.

Firstly we shall be looking at the site excavation report of the cult site of Invernesk. A study of the actual cult site remains will hopefully allow us to formulate some semblance of conception of understanding when it comes to the ever allusive and mysterious cult. In terms of textual primary source evidence, we have very few avenues to explore, due to the secretive nature of the cult itself. However, I suggest you have a look at this source material, on this particular evidence compiling nature.^(1) This lack of primary textual evidence is unfortunately a double edged sword, as it contributes towards this perception of the secrecy and mysticism of the Mithraic cult, evidently leading to a veil of distortion in the overall academic understanding of the cult. The apparent secrecy and lack of documentation is most likely due to the initiate structure of the cult itself, with its members primarily consisting of soldiers in the Roman legion and merchants, along with the notable small size of the Mithraea themselves, on average holding around 30 members. This factor of the holding capacity of the Mithraea , where its identified sites are reasonably well preserved, is evident in many of the known sites of Roman Britain, from Carrawburgh to Inveresk. With the archaeological evidence of the temple site capacity, it is most likely these Mithraic cults consisted of relatively few members, which is probably why there is a very small amount of ancient literary documentation, due to the lack of widespread numbers like cult contemporaries such as that of the cult of Isis. The next dilemma in assessing the Mithraea and in turn the functions of the cult is the lack of identified examples, although there may be sites excavated and discovered, the nature of the data extracted is not necessarily beneficial towards new understanding of the cult itself. This dampener of effective data extraction of intact and well preserved Mithraea were most likely due to combination of desecration or destruction during the mid-fourth century by Christians, along with looting, and site decay. ^(2) These dilemmas, as all archaeologists routinely face, are continued to be mired and compounded through years of misinterpretation, most notably within the publications of the early twentieth century. In particular within the Belgian archaeologist, Franz Cumont’s work of Textes et Monuments Figurés Relatifs aux Mystères de Mithra, which proposed that the Roman cult of Mithras was merely an emulation of an ancient Indo-Persian deity known as Mithra. ^(3)Alas we go down the wonderful rabbit hole that is academic discourse as we arrive to his interpretive proposal being disproven in 1971 during an international conference of Mithraic studies, which instead supported a Roman origin of the Mithraic cult. This academic shift came to fruition after the publication of Corpus Inscriptionum et Monumentorum Religionis Mithriacae, by Cumont’s student, Martin Vermaseren in 1956. Vermaseren’s publication included the archaeological evidence of Mithraic cult sites over the last 50 years, which in turn did not support Cumont’s initial theory.^(4) This is a significant factor within the dilemmas of assessing the archaeological remains of Mithraic sites as it shows how lack of archaeological and ancient literary evidence can not only lead to an incorrect interpretation, but can also lead to a shift in a collective academic perspective. However, with an advance of technological methods utilized by archaeologists currently, recent excavations of these Mithraic sites can now offer an even greater insight to scholars. Hence why I adore archaeology, as you get to occasionally play with lasers and 3D printers!

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>Continued on in the next comment!

This old post by u/Zaedert is excellent: https://www.reddit.com/r/AskHistorians/comments/6gpk65/what_was_mithraism_why_was_it_so_popular_in_the/disl7e4?utm_source=reddit-android