This question is problematic, which I will try to address, but I'm going to point you to the links on my profile page to give you some reading material with citations to add to this since I don't have time to list out all my sources tonight.

First off, the Kamakura period (1185-1333) was not feudal. At no point in premodern Japanese history would I comfortably call Japanese society "feudal". There was a semi-separate "warrior government" with retainers, who, if you stretch it, might be considered "vassal"-like, but they were not bound to serving the shogun - who, additionally, was a puppet controlled by the Hojo family. They received rights to work on certain lands, or had those rights confirmed, by the shogun/Hojo, but they could, and did, just as easily get them confirmed by the emperor/any aristocrat they could find in Kyoto. That is not a feudal system.

Civilians did not exist in premodern Japan. The concept is a modern construct, but I assume you're using it to differentiate "warriors" and "non-warriors", and further separate "non-warriors" into "non-elites". It's not that clear-cut. Warriors were both elites and non-elites. Non-elites were warriors, agriculturalists, and artisans. Artisans were both warriors and aristocrats. At any time prior to the Edo period codification of class, social positions were incredibly fluid. Economic and social resources did, in many ways, create elites and non-elites, but those were "classes" or "castes". They were those with more or less resources. The only strict social clubs were the inner circle of courtiers of the highest ranks and those retainers who had their rights confirmed by Minamoto Yoritomo, which was largely a matter of producing the right (or faked) document when asked because nobody kept a list. Even the high ranks were fairly fluid, as we see when Go-Daigo is emperor in the 1320s, and especially in the later part of his rule.

To address what I think is the core of your question, unfortunately there isn't much written on it. Nothing in English (yet, though I know someone working on artisans in later centuries), and it's not a primary focus in Japanese. There were certainly artisans (referring to your comment addition), and they worked in a wide variety of social positions. You have artisans with court ranks (elites), prosperous artisans without rank (non-elites), and those working for them. It's actually a really fascinating topic. Unfortunately, while there are a ton of documents left from this period, most of them are legal disputes or affirmations of rights/service reports. There are some confirmations of rights of artisan groups to work in certain areas, but my understanding of these is that they're from the 16th century, and the only ones I've seen that claim to be from earlier are forgeries. It might be significant that there was enough of a tradition of artisan trading rights to claim that Yoritomo verified them in 1190 or whatever, but I think the sketchiness of the documents we have is part of why there's not much written about it.