But the gemara only seems to be saying that a non-Jew may not cease his productive employment out of laziness [sheshavat] (the Schottenstein reads "an idolater who ceased working for an entire day" as opposed to the translation in the linked answer which reads "A heathen who keeps a day of rest" and this answer which reads " A non-Jew who observes Shabbos"). In fact, the Schottenstein explains Ravina's elaboration that even a Monday would qualify to point out that the issue is not the religious observance of the Sabbath but any choice not to work for any day.
The Rambam says (in Hilchot Melachim 10:9) "וכן גוי ששבת--אפילו ביום מימות החול--אם עשה אותו לעצמו כמו שבת" a non-Jew sheshavat, even on a weekday. He then explains "if he made it for himself as a Sabbath" so the reasoning has to be religious: he did it for religious reasons but not as part of observing a Jewish sabbath. He continues "אין מניחין אותן לחדש דת, ולעשות מצוות לעצמן מדעתן" "They are not to be allowed to originate a new religion or create mitzvot for themselves based on their own decisions" (translation from here). The Rambam also says a line later, "If a gentile studies the Torah, makes a Sabbath, or creates a religious practice, a Jewish court should beat him, punish him, and inform him that he is obligated to die." This is at odds with Ravina's statement but can't be a blanket condemnation of all Torah related behavior of the non-Jew because a convert can study the Torah, at least parts of it. It also can't be a blanket condemnation because the Rambam, then writes, "We should not prevent a gentile who desires to perform one of the Torah's mitzvot in order to receive reward from doing so, provided he performs it as required." He is not creating a religious practice, just following Jewish law, so it is OK (and he doesn't say "except for observing the Sabbath).
So the problem according to the Rambam still has to be doing these things in an effort to create his own religious practice, not in an effort to observe them as mitzvot.
So how do these two sources (one about laziness and one about crafting a new religion) develop into the idea that a non-Jew who wants to rest or observe the Sabbath (as part of a process of Jewish belief, or at least, not in an expression of laziness) is not allowed to? I don't see a citation to the Shulchan Aruch in this regard. No where in the gemara's statement is there mention of melacha being the issue so carrying a pen wouldn't address Ravina's point and if one was in the process of converting, the Rambam's concern wouldn't be present.
The other aspect, that the Sabbath is a unique covenant between God and the Jews so non-Jew cannot participate in it, seems not to connect with either of the potential sources. And since observance requires both Shamor and Zachor, a non-Jew should be able to "rest" completely and just not make Kiddush.
Then how/where did the statement of the gemara and the Rambam turn into the conventional wisdom which leads to jokes like this? How did a concern about laziness or about making a new religion turn into a prohibition against keeping a sincere and proper Sabbath on the path to conversion?