Crystalline mercury sulfide exists in two drastically different polymorphic forms in different domains of the P,T-diagram: red chain-like insulator alpha-HgS, stable below 344 degrees C, and black tetrahedral narrow-band semiconductor beta-HgS, stable at higher temperatures. Using pulsed neutron and high-energy X-ray diffraction, we show that these two mercury bonding patterns are present simultaneously in mercury thioarsenate glasses HgS As2S3. The population and interconnectivity of chain-like and tetrahedral dimorphous forms determine both the structural features and fundamental glass properties (thermal, electronic, etc.). DFT simulations of mercury species and RMC modeling of high-resolution diffraction data provide additional details on local Hg environment and connectivity implying the (HgS2/2), oligomeric chains (1 <= m <= 6) are acting as a network former while the HgS4/4-related mixed agglomerated units behave as a modifier.