The gene regulatory networks (GRNs) underlying specification of multipotent progenitors to different lineages remain poorly characterised. Using the zebrafish neural crest (NC) and its derivative pigment cell lineages as a model and employing a previously established systems biology approach, we set out to construct GRNs governing fate segregation of multipotent NC progenitors. Here, we present data used to construct the core specification GRN for the iridophore, one of the zebrafish chromatophore lineages. Mutant phenotypes identified the transcription factors Sox10, Tfec and Mitfa as well as the receptor tyrosine kinase Ltk as key players. Regulatory interactions were derived using chromogenic in situ hybridisation on wild-type and mutant embryos, but also by overexpressing each gene and measuring resulting changes in gene expression by qRT-PCR. Our data supported the crucial role of a sox10-dependent positive feedback loop between tfec and ltk, driving iridophore specification. Establishment of the core network topology was followed by mathematical modelling using a system of differential equations solved numerically in MATLAB. The biological relevance of the predicted gene expression dynamics was experimentally assessed and testable hypotheses were derived to improve the model’s accuracy. Using cycles of theoretical testing and experimentation, we improved and expanded the GRN by identifying previously overlooked regulatory mechanisms and additional factors. For example, we propose that a threshold level of Ltk signalling is required to enable tfec upregulation. Moreover, we discovered that sox10 expression remains upregulated throughout iridophore development, leading us to investigate candidate repressors of its melanocyte-specific downstream target, mitfa. Although Foxd3 is reportedly suppressing mitfa, we present in situ hybridisation, as well as ltk/foxd3 co-expression data obtained by the novel and highly sensitive fluorescent labelling RNAscope technique, that surprisingly challenge the proposed ongoing role of Foxd3 in the lineage. We conclude that Foxd3 is unlikely to be the repressor of mitfa in this context, while the lack of iridophores observed in foxd3 mutant embryos likely results from a role in earlier NC progenitors. Overall, our studies shed light on NC development and demonstrate the value of integrating experimental and mathematical approaches when investigating complex networks.