A primary goal of biogeography is to understand how large-scale environmental processes, like climate change, affect diversification. One often-invoked but seldom tested process is the so-called ''species-pump'' model, in which repeated bouts of co-speciation is driven by oscillating climate-induced habitat connectivity cycles. For example, over the past three million years, the landscape of the Philippine Islands has repeatedly coalesced and fragmented due to sea-level changes associated with the glacial cycles. This repeated climate-driven vicariance has been proposed as a model of speciation across evolutionary lineages codistributed throughout the islands. This model predicts speciation times that are temporally clustered around the times when interglacial rises in sea level fragmented the islands. Given the significance and conceptual impact the model has shown, surprisingly few tests of this prediction have been provided. We collected comparative genomic data from 16 pairs of insular gecko populations to test the prediction of temporally clustered divergences. Specifically, we analyze these data in a full-likelihood, Bayesian model-choice framework to test for shared divergence times among the pairs. Our results provide support against the species-pump model prediction in favor of an alternative interpretation, namely that each pair of gecko populations diverged independently. These results suggest the repeated bouts of climate-driven landscape fragmentation has not been an important mechanism of speciation for gekkonid lizards on the Philippine Islands. Interpretations of shared mechanisms of diversification historically have been pervasive in biogeography, often advanced on the basis of taxonomy-based depictions of species distributions. Our results call for possible re-evaluation of other, classic co-diversification studies in a variety of geographic systems.