The rising global warming concerns make it inevitable to phase out fossil fuels sooner rather than later, as they contribute to about 60% of the greenhouse gas emissions in the world. One alternative to fossil fuels in heavy industry is green hydrogen. However, hydrogen combustion in air is known to emit the oxides of nitrogen (NOx) which are harmful to health. An improved comprehension of these NOx emissions and their formation pathways is the first step towards their mitigation. This paper intends to improve the methodology to understand the NO formation pathways in a non-premixed, swirl-stabilised, hydrogen/air gas-turbine combustor. To do so, high-fidelity large-eddy simulations (LESs), extended proper orthogonal decomposition (EPOD) technique and zero-dimensional (0D) perfectly stirred reactor (PSR) analyses are combined to utilise the merits of each of these techniques. While the LES ensures that the flow-field and reactions are well captured, EPOD is applied to identify two points featuring high positive and high negative fluctuations of the rate of production of NO, i.e. ROPNO, respectively. The 0D PSR provides a platform for a cost-effective yet detailed chemical pathway analysis at these identified points. Although both NO production and consumption reactions are prevalent at the chosen points, the net effect is that of NO production as was evidenced by the positive value of ROPNO at these points. However, the rate of production of NO differed between the two points. While the major NO formation and consumption reactions were found to be the same at both the points, their contributions to overall ROPNO varied. The major NO production reaction at both the points was NNH+O NH+NO, contributing to 37% and 26% at the points with high positive and high negative ROPNO fluctuations, respectively. Moreover, the species composition was different at the chosen points, which is expected in a non-premixed combustion configuration. For instance, the mass fractions of NNH and O, i.e. the reactants in the major NO production reaction, were respectively 18.28% and 8.77% higher at the point with high positive ROPNO fluctuation compared to the point with high negative ROPNO fluctuation. The above-mentioned differences in the reactions' contributions to ROPNO at the chosen points could be attributed to such variation in local composition, which is highly likely in non- premixed combustion. The methodology proposed in this paper enables a detailed chemical pathway analysis emphasising the points featuring high ROPNO fluctuations. This technique, which conducts a focused analysis of the NO formation pathways in a combustor, can be a useful tool in the effort towards designing cleaner hydrogen combustors.