which引导的是定语从句，定语从句的主干是which is the nearest.

they will ever get to thought也是定语从句，关系词是that（句中作宾语，故可以省去）,先行词是mental process（句中因跟主语相同，故可省去）。不过它是从属于which引导的定语从句，即相对而言which is the nearest是主句，(that) they will ever get to thought是从句。

把省略的东西都加上去之后就是：

I no longer dismiss lightly a mental process which for nine tenths of the population is the nearest(mental process)(that) they will ever get to thought.