Multistable gene regulatory systems sustain different levels of gene expression under identical external conditions. Such multistability is used to encode phenotypic states in processes including nutrient uptake and persistence in bacteria, fate selection in viral infection, cell-cycle control and development. Stochastic switching between different phenotypes can occur as the result of random fluctuations in molecular copy numbers of mRNA and proteins arising in transcription, translation, transport and binding. However, which component of a pathway triggers such a transition is generally not known. By linking single-cell experiments on the lactose-uptake pathway in E. coli to molecular simulations, we devise a general method to pinpoint the particular fluctuation driving phenotype switching and apply this method to the transition between the uninduced and induced states of the lac-genes. We find that the transition to the induced state is not caused only by the single event of lac-repressor unbinding, but depends crucially on the time period over which the repressor remains unbound from the lac-operon. We confirm this notion in strains with a high expression level of the lac-repressor (leading to shorter periods over which the lac-operon remains unbound), which show a reduced switching rate. Our techniques apply to multistable gene regulatory systems in general and allow to identify the molecular mechanisms behind stochastic transitions in gene regulatory circuits.