I've tossed 20+ wishing pieces into the well to the right of Hammerlock's entrance without any success. Now I'm wondering if it is possible for that well to spawn rare beams or at all, or did I just have a run of bad luck?
Every Den should be able to spawn an rare beam. If you look at Serebii you can find a detailed list with all the Pokemon 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 Pokemon. If you click on the den you can see which Pokemon spawns at what percentage.
If you have troubles 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 Pokemon. 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.