The Cleopatra Problem
If I had a dollar for everyone who thinks they were Cleopatra or Alexander the Great in a past life then I’d be considerably wealthier. Having worked with many people to help them recover their previous reincarnations I can say that we have found many more ordinary folks than famous ones. However getting a flash of a previous incarnation can be a surprising and powerful experience and there is a natural tendency for people to jump to conclusions. For example, someone is working with recovering past-lives and recovers a memory of being by a river and seeing some pyramids – that must mean I was Cleopatra back in the day right? No, those pyramids have been around for quite a while. You may have been a farmer, a fisherman or a slave and seen exactly those sights. Remember the guy who swept the floor also sees the throne. These recognizable bits are good starting points but it's better to use them as a base rather than seeing them as "proof".
There doesn’t seem to be any link between how “important” a person was and their ability to recover past lives. What does seem to make a difference is having practice and training of a spiritual nature. That is normally associated with lay or priestly activity.
There is also the (mainly) USAn issue of people who "were Indian in a previous life". The extent to which that's an entirely authentic recovered memory or part a romantic day dream may differ for each individual. If indigenous First Nation peoples in the USA are in bulk reincarnating as modern middle class white folks it's not for me to say. I doubt it's simply a binary choice, but one of the key indicators of a real recovered memory is not the duration of the memory but its detail, these are often mundane details of domestic life but can include times of high emotion such as childbirth and violent death. The assertion that "I was x in a previous life, so..." can be simply self-serving and we should be honest in that. This takes us into areas like cultural appropriation which is a large and contentious issue. (try the following for a view from a Native American on this. http://www.thepeoplespaths.net/articles/formlife.htm).
However what I would say is that Mithraism is a path for recovering the self and preparing for the continuity of the self. It therefore increases the probability that you've been doing this for more than one life.