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As for how Honey trees work, first you need Honey.
You can find some as items, but the guy in the Floaroma Meadow sells them and is the easiest replenish-able source of honey.
When you have Honey you literally just walk up to a Honey tree and interact with it. Slather on some Honey and then you need to wait.
I think it's 6 hours before something starts showing up and you have 24 hours to check on the tree before whatever showed up disappears again.
There is also a chance of nothing showing up as one of the Honey trees I slathered yesterday didn't have anything show up at all D=
It's important to keep in mind that changing the Switch clock data or playing it in another Switch will lock time events for 24 hours, so you need to wait for those 6 h the legit way.
You just turn the game off and do the encounter again until a shiny appears! Similar to how you shiny hunt most other things. Just have to keep in mind that honey spawns disappear after 24 hours, so if it takes you longer than that to find a shiny, you'll need to start over again. :(