Kimura shows that selection can play little or no role in the generation of variation.
Nah! He doesn't show that. He echos and supports that idea from basic biology, genetics, and population genetics. Selection is one of the mechanisms of evolution that tends to eliminate variation in populations. It does this because favorable variation in light of the surrounding environment lends differential reproductive success. The idea is most definitely not original with Kimura.
(Genetic) drift, by the same token, tends to eliminate variation. As Wounded King has pointed out, the smaller the population, the more likely it is that novel variations will be eliminated. The founder effect, a special case of genetic drift, is understood to be causal in the speciation of small island populations.
There are other commonly recognized mechanisms that tend to reduce variation in populations, biased variation and non-random mating. Of course there are also mechanisms that tend to increase variation: mutation, gene flow, transposable elements, and recombination.
Others may be able to list other, less obvious, mechanisms.