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  1. Context. Models of stellar structure and evolution can be constrained using accurate measurements of the parameters of eclipsing binary members of open clusters. Multiple binary stars provide the means to tighten the constraints and, in turn, to improve the precision and accuracy of the age estimate of the host cluster. In the previous two papers of this series, we have demonstrated the use of measurements of multiple eclipsing binaries in the old open cluster NGC 6791 to set tighter constraints on the properties of stellar models than was previously possible, thereby improving both the accuracy and precision of the clustermore »age. Aims. We identify and measure the properties of a non-eclipsing cluster member, V56, in NGC 6791 and demonstrate how this provides additional model constraints that support and strengthen our previous findings. Methods. We analyse multi-epoch spectra of V56 from FLAMES in conjunction with the existing photometry and measurements of eclipsing binaries in NGC6971. Results. The parameters of the V56 components are found to be M p  = 1.103 ± 0.008  M ⊙ and M s  = 0.974 ± 0.007  M ⊙ , R p  = 1.764 ± 0.099  R ⊙ and R s  = 1.045 ± 0.057  R ⊙ , T eff,p  = 5447 ± 125 K and T eff,s  = 5552 ± 125 K, and surface [Fe/H] = +0.29 ± 0.06 assuming that they have the same abundance. Conclusions. The derived properties strengthen our previous best estimate of the cluster age of 8.3 ± 0.3 Gyr and the mass of stars on the lower red giant branch (RGB), which is M RGB  = 1.15 ± 0.02  M ⊙ for NGC 6791. These numbers therefore continue to serve as verification points for other methods of age and mass measures, such as asteroseismology.« less