Geographic barriers can come and go depending on natural conditions. These fluctuations cause population cycles of expansion and contraction, introducing intermittent migrations that may not hinder speciation but rather promote diversification. Here, we study a neutral two-island speciation model with intermittent migration driven by sea-level fluctuations. Seabed depth modulates isolation and connection periods between the islands, with migration occurring during connection periods with a certain probability. Mating is restricted to genetically compatible individuals on the same island, and offspring inherit genomes from both parents through recombination. We observe speciation pulses that would not occur under strict isolation or continuous migration, with infrequent, temporary increases in species richness happening at different times depending on the combination of geographic settings and migration probability. The resulting dynamic patterns of richness exhibit contrasting behavior between connected and isolated scenarios, often including species that do not persist.  Prolonged isolation can reduce richness to one species per island, resembling patterns commonly associated with archipelagos under sea-level fluctuations. Together with other studies, our results in out-of-equilibrium populations support the relevance of investigating the impact of variable migration on diversification, particularly in regions of high diversity.