Mechanism(s), it's going to be highly polygenic & mediated through many pathways. I don't see it as needing to be any more inherently mysterious than appendicitis: it's all cells doing very complicated chemical stuff in long causal pathways, in the end. 'Appendicitis' need be no more 'direct' or 'simple' than 'alcoholism'.
For example, I expect that I have a very low genetic risk for alcoholism - no family history, and drinking more alcohol than a beer or two makes me miserably depressed. There is surely some sort of neurochemical explanation there, something something GABA depressive neurotransmitter positive reinforcement of alcohol-avoidance behavior yadda yadda, but the net effect is the same: I'm not going to become an alcoholic. If you could trace it out, it's not going to look any more mysterious than some appendicitis explanation starting with an immune-modulating SNP affecting T-cells modifying risk of random hepatitis virus infecting the appendix and triggering an autoimmune reaction... or whatever it is that is between 'SNP variant #123' and 'developed appendicitis at age 14'. It's all cause-and-effect, atoms-and-void, in the end.
Alcoholism is that heritable: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4345133/ At ~50% heritability, it is in no way unusually low, and entirely comparable with many other traits.