Earlier quoted context omitted.
How about, "after decades of searching using all of the best available tools, none has been found".
We know that some mental illnesses have a genetic component. How would that happen if there were not something physical? Just because we don't know now, doesn't mean we will never know. That's how science works.
People have 'mental illness' because of mental problems, not physical problems.
Also: everything has some genetic component, this is trivially true. Genetics are what separates humans from dogs and plants. It doesn't necessarily help us to explain the phenomenon adequately.
Also also: another way science works is its inability to prove negatives. Therefore, saying, "someday we might discover this" can be said for pretty much anything that remains unproven.