Charism of Carmel
First of all, material on the topic is scarce. Whereas I could find three versions of the Rule of St. Benedict online within a minute, it took a lot more digging to find out what rule, if any, governed Carmel (the Rule of St. Albert). Reading lists for Third Order Secular Carmelites consisted almost exclusively of the Carmelite Constitutions, the St. Teresa of Jesus/Avila and St. Therese of Lisieux, and St. John of the Cross.
What I did find on the Carmelite vocation made it sound deceptively simple...an emphasis on achieving divine union with God through private prayer as exemplified by the image of Jesus praying alone in the garden of Gethsemane, an apostolate focused first and foremost on such private prayer, a Marian devotion upholding Mary as an exemplar of contemplation evidenced by the Scriptural description of Mary as "pondering all these things in her heart." There was not even a specifically prescribed method for the "mental prayer" around which their daily lives revolve. That is left to the individual.
As I read more and more Carmelite writings, some of which I had to order from as far away as England, these themes repeated themselves. I found the writings of St. John of the Cross, especially Ascent of Mount Carmel, far easier reading than Thomas Merton's intellectually dense commentary on it, The Ascent to Truth. Their charism still sounds deceptively simple, but the practice associated with it is not necessarily easy.
As for culture, the ongoing Carmelite formation expectations seem tailored to the mentally gifted and highly motivated. Further, the religious Carmelites seem uniquely inaccessible, even to their oblates, a far cry from the open-armed Benedictine and Franciscan hospitality I've been accustomed to. The one Carmelite monastery within driving distance of my home, and not a short distance, doesn't even have information about the seculars associated with their monastery on their website, as beautiful as that website is, nor do the seculars have a website at all.
But I have yet to interact personally with any lay or religious Carmelites, mostly because I have yet to determine that such a move would be advantageous to the development of my practice, which seems to falter every time I try to formalize it based on an external structure.