There isn't anything in specific for tatooing on any body part. By tattooing on left shoulder, it could mean that the particular symbol is close/dearer to your heart.
It means you are sane. The brain's right hemisphere controls your body's left side. By tattooing your right shoulder, you would not have been in your right mind.
A lot of people get tattoos in places that have a special meaning to them. Some people may be left handed and that is why they choose to get a tattoos on the left side of their body. It is really a personal decision.
I got my right shoulder tattooed so it would be seen more often. Since I carry my bag's over my left shoulder the straps would have covered some of it if I'd had it done on my right side. Just personal preference I guess
It depends on the tattoo. I have one between my shoulder blades that I got with my sister. It symbolises that my sister has my back. Idk. It really depends.