This is probably reaching but --
Furuta’s Birthday is the Leap Year, written
Which has the kanji for King 王 underneath the Kanji for gate/door 門. That’s been covered [x]
But here’s Amon’s name in Kanji
That first Kanji, 亜, is used for the prefix “sub-”. So “Amon” written as 亜門 can be read as “under the gate/door” which is where the leap year’s King kanji is.
Does this mean the King that Furuta has been looking for is Amon? Furuta seems not to have considered Kaneki, so perhaps he is looking for someone else, though he claims not to care anymore.
Seeing as the One-Eyed King isn’t actually some mystically appointed title, but a figure that people must believe in and follow and thus choose themselves, perhaps despite Kaneki’s claim of the throne, there may be another (or several other) Kings at play.
Does this crazy word game imply that Furuta and Amon will be together in this? Opposed?
Considering Furuta’s involvement with Kanou and his willing participation in the deaths of hundreds, I doubt Amon, at least as we knew him, would consider him a willing ally.
But things are quite a mess right now, and the Clowns including Donato are on the move, a group that now unifies both of them.
Or this could be me, someone who knows basically no Japanese and is a little bit loopy right now, having too much fun with Kanji. Who knows?
Only Ishida. Only Ishida knows...