Genes go back as far as you can trace them.
OK quick genetics 101 lesson:
There are many different patterns of inheritance, the simplest and most obviously straightforward being Mendelian autosomal dominant and autosomal recessive. For each gene that a person has, it comes in a pair, either the same or of the alternate.
say you're looking at inheriting blue eyes:
Gene A = brown eyes (the dominant phenotype)
Gene a = blue eyes (the recessive phenotype)
Say mom has brown eyes and dad has blue eyes.
Mom's genotype could be AA or Aa (for the dominant gene you only need one of the pair to be that gene, to express that phenotype).
Dad's genotype is aa for sure (recessive phenotype only shows up if both genes are present)
So, if Mom's genotype is AA, there is a 25% chance they will have a kid with blue eyes. If Mom's genotype is Aa, there is a 50% chance their kid will have blue eyes.
There are also such patterns of inheritance as incomplete penetrance (which is more like how skin color is inherited), gene linkage, X-linkage, etc which are way beyond the scope of a rudimentary explanation.
Obviously socionics heritability is a LOT more complicated than the blue eyes scenario, and obviously does not happen by a simple Mendelian autosomal pattern. Heck I'll bet there are a whole bunch of genes involved in expression of each particular sociotype. And I wouldn't be surprised if there is an incomplete penetrance sort of thing involved. Moreover, I do believe that sociotype is multifactorial, and not purely genetic. For one, my identical twin sister and I (who share an identical genome) are pretty obviously different sociotypes.
My mother: likely SEE
My father: not sure, I think SLE
Sister: LII or EII
Me: IEE