The corpus's first Sharingan mention (Vol. 2 p.84) doesn't even wait for a clean introduction — an enemy ninja recognizes Kakashi mid-fight and blurts "しゃりんが写輪眼のカカシがいたんじゃなァ" ("IT'S KAKASHI... KAKASHI OF THE SHARINGAN EYE!"), and the reveal panel six pages later (used for this entry's crop) has Sasuke visibly shaken: "写輪眼!?" rendered "THE SHARINGAN— THE MIRROR-WHEEL EYE?!" That page is doing the same double-duty translation the corpus shows for several other dojutsu in this dictionary (compare Byakugan's "ALL-SEEING EVIL EYE" gloss): VIZ clearly didn't trust readers to absorb a bare loanword cold in Volume 2, so it pairs the romanized brand name with a literal English gloss for a few pages of introduction (Vol. 2 pp.90–95: "MIRROR WHEEL EYE," "MIRROR-WHEEL, OR SHARINGAN, EYE") before retiring the gloss entirely by Vol. 7, where "写輪眼〆" simply becomes "SHARINGAN!!" — no scaffolding needed once the term has stuck.
Mangekyo Sharingan gets no such hand-holding at all. Its first corpus appearance (Vol. 16 p.145) is mid-conversation, translated as bare "MANGEKYO" with no gloss, and by Vol. 17's first full shout ("万華鏡写輪眼〃" / "MANGEKYO SHARINGAN!!") the two words are simply stapled together as one romanized compound — VIZ apparently decided by this point in the run (roughly four years into serialization) that its readership could handle new terminology without training wheels. The irony is that 万華鏡 (kaleidoscope) is one of the few Sharingan-family terms with a perfectly natural, exact English equivalent, and VIZ chooses not to use it even once in the sampled occurrences — Itachi's own explanation of how he awakened it (Vol. 25 p.133, "それがまさに万華鏡写輪眼がある" / "...IT'S CALLED MANGEKYO SHARINGAN") treats the compound as a fixed proper noun, not a description to translate.
写輪眼 is the single most cited term in this entire signature-jutsu set — 235 corpus mentions for the base Sharingan alone, plus 63 for Mangekyo, 298 combined — which tracks with how the ability functions as a plot engine across nearly the whole manga: every major Uchiha character, plus Kakashi, is defined by which stage of Sharingan they carry. The Vol. 70 crossover hit sampled here ("母は白眼以外に写輪眼の力をも有していた" / "MOTHER POSSESSED THE POWER OF SHARINGAN AS WELL AS BYAKUGAN") is a late-series reveal that briefly merges this entry's bloodline with the Hyuga's — worth cross-referencing against the Byakugan entry in this dictionary.