Supermassive black holes require a reservoir of cold gas at the centre of their host galaxy in order to accrete and shine as active galactic nuclei (AGN). Major mergers have the ability to drive gas rapidly inwards, but observations trying to link mergers with AGN have found mixed results due to the difficulty of consistently identifying galaxy mergers in surveys. This study applies deep learning to this problem, using convolutional neural networks trained to identify simulated post-merger galaxies from survey-realistic imaging. This provides a fast and repeatable alternative to human visual inspection. Using this tool, we examine a sample of ~8500 Seyfert 2 galaxies ($L[\mathrm{O\, {\small III}}] \sim 10^{38.5 - 42}$ erg s-1) at z < 0.3 in the Sloan Digital Sky Survey and find a merger fraction of $2.19_{-0.17}^{+0.21}$ per cent compared with inactive control galaxies, in which we find a merger fraction of $2.96_{-0.20}^{+0.26}$ per cent, indicating an overall lack of mergers among AGN hosts compared with controls. However, matching the controls to the AGN hosts in stellar mass and star formation rate reveals that AGN hosts in the star-forming blue cloud exhibit a ~2 × merger enhancement over controls, while those in the quiescent red sequence have significantly lower relative merger fractions, leading to the observed overall deficit due to the differing M*-SFR distributions. We conclude that while mergers are not the dominant trigger of all low-luminosity, obscured AGN activity in the nearby Universe, they are more important to AGN fuelling in galaxies with higher cold gas mass fractions as traced through star formation.