The goal of this work is to assess the mechanistic bases of natural genetic variations in plant responses of photosynthesis to stress. To achieve this goal, we devised the Linkage Integration Hypothesis Testing (LIgHT) approach, comparing chromosomal locations of quantitative trait loci (QTL) for multiple phenotypes to distinguish between hypothetical mechanisms. As a use case, we explored genetic variations in photosynthesis-related processes under chilling stress in recombinant inbred lines of cowpea (Vigna unguiculata L. Walp.). We focused on photosynthesis-related parameters measurable in high throughput and indicative of proposed chilling responses, including the states of photosystems I (PSI) and II (PSII), photoprotective nonphotochemical quenching, PSII photodamage, and nyctinastic leaf movements (NLM). The patterns of QTL linkages indicated chilling stress tolerance is genetically controlled by avoiding PSII photodamage rather than PSI damage or NLM. This model was validated in a separate experiment measuring the rates of PSII photodamage and repair. Additional linkages suggest that chilling-induced damage to PSII is controlled by the thylakoid proton motive force and redox state of PSII. This regulation is modulated by thylakoid fatty acid composition, as suggested in Hoh et al., 2022. We propose the LIgHT approach can be broadly applied to test mechanisms underlying genetic variations.