We report measurements of resolved (CH2D2)-C-12 and (CH3D)-C-13 at natural abundances in a variety of methane gases produced naturally and in the laboratory. The ability to resolve (CH2D2)-C-12 from (CH3D)-C-13 provides unprecedented insights into the origin and evolution of CH4. The results identify conditions under which either isotopic bond order disequilibrium or equilibrium are expected. Where equilibrium obtains, concordant Delta (CH2D2)-C-12 and Delta (CH3D)-C-13 temperatures can be used reliably for thermometry. We find that concordant temperatures do not always match previous hypotheses based on indirect estimates of temperature of formation nor temperatures derived from CH4/H-2 D/H exchange, underscoring the importance of reliable thermometry based on the CH4 molecules themselves. Where Delta (CH2D2)-C-12 and Delta (CH3D)-C-13 values are inconsistent with thermodynamic equilibrium, temperatures of formation derived from these species are spurious. In such situations, while formation temperatures are unavailable, disequilibrium isotopologue ratios nonetheless provide novel information about the formation mechanism of the gas and the presence or absence of multiple sources or sinks. In particular, disequilibrium isotopologue ratios may provide the means for differentiating between methane produced by abiotic synthesis vs. biological processes. Deficits in (CH2D2)-C-12 compared with equilibrium values in CH4 gas made by surface-catalyzed abiotic reactions are so large as to point towards a quantum tunneling origin. Tunneling also accounts for the more moderate depletions in (CH3D)-C-13 that accompany the low (CH2D2)-C-12 abundances produced by abiotic reactions. The tunneling signature may prove to be an important tracer of abiotic methane formation, especially where it is preserved by dissolution of gas in cool hydrothermal systems (e.g., Mars). Isotopologue signatures of abiotic methane production can be erased by infiltration of microbial communities, and Delta (CH2D2)-C-12 values are a key tracer of microbial recycling.