Having finally read all of the Harry Potter books (in 3 weeks only) the best answer I can think of regarding the nature of magic inheritance is that the magic phenotype is a quantitative trait, like height. As with height, part of how tall a person is is partly determined by genetics but a part of it is also determined by one's environment: medicine, nutrition, stress, etc. Its the only way possible to explain how some witches/wizards are just more powerful than others. Additionally, it also nicely explains why two pure bloods who are competent at magic can have an offspring who is a squib.
As for the magic gene, I would think that it would actually be genes. Something as complicated as magic could not possibly be controlled by one single gene, there has to be several genes expressed.
Harry Potter - wizard breeding
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