MeiTanteixX

Rum specifically wasn't shown to be wary of either or. We just know the BO as a whole had their attention on both cases, because it's connected to Rum's mistake. As for Hotta, he wasn't shown to be an "allowed"/dismissed Kohji case investigator by BO. We just didn't follow the BO perspective in regards to his Kohji case segment announcement (except at the very end through Gin & Vodka after his death), as we did through Bourbon & Vermouth with Rokumichi's ASACA song announcement.

Oooka & Haneda household connection Recent development from File 1042 makes Iori Muga even more suspicious, since we now found out that the Haneda household is a wealthy associate of the Oooka household. His position as a Butler for the Oooka, who seems to be trusted and relied on by the Haneda, makes for a perfect information source (without getting too close to the target) about what they know about the Kohji case and what they are up to, to cover for his 17-year-old mistake (File 953), especially if RUM suspects (naturally) that the Haneda family are behind the repeated Kohji case information upload online (File 948) which the BO keeps taking down.

I actually have a theory which fits with his seemingly confirming reply to SDB BLACK+ Q92 “Is Rum certainly amongst the trio Kuroda, Wakasa & Wakita?”. I don’t actually think it’s as straightforward as he made it seem. I think that his reply stems from the fact that... "Wakita Kanenori = Highball" Theory In other words, from my perspective, Gosho is pulling another misleading comment like he did with Animal Crossing for File 906 (where "Rum" he is thinking of is not the same as the one you would originally think), where he had said “Rum has actually already appeared (laughs)” (which was actually referring to Lum).

Hyoue's impatience portrayal while talking to Yamato is certainly incriminating, but then again, that's a part of a package of obvious Rum portrayal, and we certainly haven't seen that side more than once. I don't think however that Rumi and Wakita has acted unusually, or unjustifiably, impatient. I think their time is yet to come, considering how fresh that newly established intel on Rum is. In comparison however, Iori's obsession of time is definitely much clearly defined and distinguishable (as you said, counting seconds) through his continues attention on it during mulitple matters.

Rum impatience and time sensitivity VS Iori Muga impatience and time sensitivity

Wakasa Rumi's memories Wakasa Rumi's pain Conan's fake identity examples

Indeed ^^ Thank you

Click "edit", select everything that you want to surround in spoilers, click on the eye symbol for "spoiler". And then "save changes".

Rei & Shiho

the long frequent breaks is so that Gosho doesn't overwork himself and worsen his health, since he has had a lot of health issues (like many Mangakas) due to overworking (a common thing in the japanese culture). He used to sleep 3 hours a day in the last decades, but now with these long breaks between cases, he is sleeping much better.

All I can say is... there's no requirement for Rumi's piece(s) to be the exact same object(s) taken from that case because they are generic objects that aren't unique to that incident. You can find an uma piece anywhere. We can at least infer however that such knowledge was acquired by her (whether it was by directly being in possession of said objects or whether she got the info/objects second-hand). I'm pretty confident about this being an in-universe word play, much like "Mizunashi Rena"="no water (0) re (0) na (7)". My interpretation on that is straightforward. Wakita uses the idiom "Toki wa Kane nari" frequently (which without any translations was made directly into a name by rearranging letters). He is after all portrayed to be an edokko who uses japanese proverbs. Now, as for the later bit about Rum using an english version of that quote, that's a matter of what ones preconception of Rum is, if he is someone more accustomed to the english language, or if he is an edokko who for some reason decided to use it in a more out-of-character way. In the former angle, then it's possible that there's some kind of influence between Rum and Wakita that lead to both of them using the same idiom (but in their own way). In the latter angle, then that would mean that Wakita, as Rum, simply chose it because that was the name that came natural to him, because he uses its origin often, even in a different language. In the same way, if he is indeed working on Gin's behalf when it comes to Kogoro, and if he is indeed behind Mary's shrinking (as alluded to by his fitting covered left eye to Akai's left eye, which was hit by a Mary-knife-hand-strike), He is more than likely the source of the idiom "It's like encountering a demon in the darkness" as well, which could mean that he is indeed the idiom bank who (in the former angle) influences his fellow members (maybe as a high-up senior/mentor/coach figure) or (in the latter angle) simply rubbed off on Gin as second-in-command (with the latest SDB allusion of antipathy between Gin and Rum, this latter angle seems unlikely).

that, or just anyone else that got ahold of Rum's testimony, like the boss (who views Vermouth as his favorite due to some relationship). the one who pried it out of his hand could be Rum himself. that's the issue with "Wakita Kanenori". His name itself is an obvious alias derived from "Toki wa kanenari" (more than likely at least). In other words, without an actual real first name that doesn't seem like an alias, there's no method to idenitfying him as Rum through the dying message (assuming he is even Rum to begin with), and I don't see us getting a new name from him that the shogi piece + whatever remaining clues can allude to.