Troubleshooting for the "Under a Red Moon" shrine quest
A lot of websites still offer false information about how the Blood Moon works - old guesswork that was already debunked in 2017, unconfirmed rumors that were never updated, you name it.
But since the game code has been cracked and thoroughly analyzed for a couple of years now, we know exactly was does (and does not) cause Blood Moons to happen[^1] . No guesswork or trial-and-error needed when you can just look at the guts of the game itself.
Regular Blood Moons
Regular Blood Moons are on a strict schedule: 2 hours and 48 minutes [^2] of real, active playtime since the last Blood Moon happened, and nothing ever speeds up that timer, despite the ton of rumors claiming otherwise.
There are, however, two issues with that:
Only ACTIVE playtime counts. Everything that freezes the in-game time will also pause the Blood Moon timer: cutscenes, loading screens, NPC dialogue, every time you read something / make a pop-up appear, while you are in a menu or looking at the map, while you're cooking something, and of course while the software is suspended or the console turned off. You can not just put your Switch into sleep mode for 3 hours and expect a Blood Moon - it won't work.
The 2 hours & 48 minutes have to be REAL time. The in-game time doesn't matter at all, so you can not make the Blood Moon come faster by repeatedly skipping nights at a campfire or solving quests that automatically fast-forward the time (like the Stolen Heirloom). The in-game moon phases also do not matter: The Blood Moon will always appear as a red full moon, no matter which moon phase was actually due that night.
With these two issues in mind, there can be huge discrepancies between the expected ~ 3 hours worth of playtime and the time that actually "counts".
Example: You just talked to Dorephan, Vah Ruta emerged from the East Reservoir, the Zora king gives you the Zora armor, Muzu storms off, you put the armor on, talk to Muzu again, get the memory flashback with Mipha, talk to Muzu again and get sent to fetch Shock Arrows ... and now you have played for half an hour but the timer only advanced during the half minute it took you to go from the Throne room to Mipha's statue, as everything else was either a dialogue, cutscene or menu.
So what SHOULD you do with this quest?
Set it aside for now and continue playing the game. If you have the Travel Medallion (DLC) then place it nearby, so that you can quickly return to the platform if there happens to be a Blood Moon. If you do not own the DLC, activate one of the fixed warp points close by (like for example the shrine on Mount Satori or the one next to Tabantha Bridge Stable).
Once each in-game day, pay Hino at the Dueling Peaks Stable a visit. He is able to predict the moon of the next night accurately: if he talks about full moon, crescent, etc. then just continue playing the game elsewhere. If he says something along the lines of "something is going to happen tonight", there will be a Blood Moon the following night, which leaves you with plenty of time to return to the platform.
If you are caught off guard by a Blood Moon, enter a shrine. It does not matter which shrine or whether or not you completed it already. Divine Beasts and Hyrule Castle work for this as well, as long as you just remove Link from the "overworld map" until in-game midnight has passed. The Blood Moon will not actually happen that same night, but instead get rescheduled to the following night, giving you another full day/night cycle to reach the platform.
If you screwed up entirely and the Blood Moon has already happened, but you do not want to wait for the NEXT Blood Moon to appear, you can reload a save file from before the Blood Moon occured. This will rewind the timer and the Blood Moon will happen again in the same night, giving you a grace period to either reach the platform or hide inside a shrine to reschedule it.
What you should NOT do:
"If you kill enough enemies and mess up the environment real bad, the Blood Moon will happen faster to reset the overworld"
... no it doesn't. Nothing ever speeds up the timer, and on top of that does the Blood Moon not "reset the overworld". The only things the Blood Moon respawns are equipment outside of chests (weapons, bows, shields) and previously slain enemies (except bosses). Everything else respawns by one of various wildly different respawn mechanisms that work independendly from the Blood Moon.[^3]
If you "mess up the game" with glitches, menu overload and the like, you might get a so-called "Panic Blood Moon" but those do not "work" like the regular ones:
Panic Blood Moons can happen at any time of the day or night, without any kind of warning, multiple times in a row and completely independent from the "Regular" Blood Moon timer. Bluntly speaking, Panic Blood Moons only happen if there is something wrong with your game and it has to reset a part of itself to prevent a crash.
However, the player does not have any kind of influence over the particular set of subsystems responsible for the Panic Blood Moon, so there is no (known) way to relieably trigger one - and even if there WAS a way to force one to happen, the Panic Blood Moon does not count for this quest, won't activate the platform, and therefore not help you in this case.
"Skipping nights at a campfire makes the Blood Moon appear eventually"
This actually makes the entire process take LONGER than before. As mentioned above, the timer pauses during cutscenes and dialogue/interactions, so the very moment you interact with the campfire the timer stops, then you select how long aou want to wait, you watch Link sit down, the screen goes dark, the music jingle plays, the sun goes up, Link stands up again .... and THEN the timer continues. You waste around 7-10 seconds every time you do this, and if you then immediatly interact with the campfire again, the timer did not advance at all. It's an easy way to turn a 3 hour waiting period into a 17 hour fiasco.
"A friend of my cousin's neighbor said that you can summon the Blood Moon by placing bananas in front of the Yiga frog statues while being naked and then twirling the C-stick real fast counter-clockwise!"
Just no. The game doesn't care what exacly you do; it won't ever fast-forward the timer or "force" a Blood Moon to appear. These rumors are just anecdotes with a hefty amount of Dude Trust Me™ garnished with misunderstanding and a sprinkle of trolling.
To say it in other words: if you keep doing random bullsh*t for 2 hours and 48 minutes then you will get a Blood Moon. But not BECAUSE you did a lot of random bullsh*t but because the timer was up. If you then reload to "check whether this tactic worked" and do the same again, then you will also get a Blood Moon, but again not BECAUSE of what you did, but because you rewinded the timer and a Blood Moon would have happened that night anyway.
Thanks man, that’s my last shrine and I’m skipping the night after I talked to Hino… again and again - no wonder why the blood moon is not coming - thank you