Can all wells spawn rare (purple) beams?

Solution 1:

Every Den should be able to spawn a rare beam. If you look at Serebii, you can find a detailed list with all the Pokémon you can encounter at any den. On the left side are the encounters for normal dens and on the right side are the rare den Pokémon. If you click on the den you can see which Pokémon spawn at what percentage.

If you have trouble finding the den you are at, try first searching for the location of the wild area you are in.

Rare dens can require a lot of luck to spawn the right Pokémon. Trying to force them with wishing pieces can take a long time. If I try the method of resetting the game before saving it, it usually takes up to 40 attempts. But if you're lucky, it can also happen within the first few tries.