In the last decade, transparent amorphous oxide semiconductors (TAOS) have become an essential component of many electronics, from ultra high resolution displays to solar cells. However, these disordered oxides typically rely on expensive component metals like indium to provide sufficient charge carrier conduction, and their optoelectronic properties are not as predictable and well-described as those of traditional, crystalline semiconductors. Herein we report on our comprehensive study of the amorphous zinc-tin-oxide (a-ZTO) system for use as an indium-free, n-type TAOS. Using a combination of high-throughput co-deposition growth, high resolution spectral mapping, and atomistic calculations, we explain the development of disorder-related subgap states in SnO2-like a-ZTO and optical bandgap reduction in ZnO-like a-ZTO. In addition, we report on a composition-induced electronic and structural transition in ZnO-like a-ZTO resulting in an exceptionally high figure of merit, comparable to that of amorphous indium-gallium-zinc-oxide. Our results accelerate the development of a-ZTO and similar systems as indium-free TAOS materials.