Context : Models of stellar structure and evolution can be constrained by measuring accurate parameters of detached eclipsing binaries in open clusters .
Multiple binary stars provide the means to determine helium abundances in these old stellar systems , and in turn , to improve estimates of their age .

Aims : In the first paper of this series , we demonstrated how measurements of multiple eclipsing binaries in the old open cluster NGC 6791 sets tighter constraints on the properties of stellar models than has previously been possible , thereby potentially improving both the accuracy and precision of the cluster age .
Here we add additional constraints and perform an extensive model comparison to determine the best estimates of the cluster age and helium content , employing as many observational constraints as possible .

Methods : We improve our photometry and correct empirically for differential reddening effects .
We then perform an extensive comparison of the new colour-magnitude diagrams ( CMDs ) and eclipsing binary measurements to Victoria and DSEP isochrones in order to estimate cluster parameters .
We also reanalyse a spectrum of the star 2-17 to improve [ Fe/H ] constraints .

Results : We find a best estimate of the age of \sim 8.3 Gyr for NGC 6791 while demonstrating that remaining age uncertainty is dominated by uncertainties in the CNO abundances .
The helium mass fraction is well constrained at Y = 0.30 \pm 0.01 resulting in \Delta Y / \Delta Z \sim 1.4 assuming that such a relation exists .
During the analysis we firmly identify blue straggler stars , including the star 2-17 , and find indications for the presence of their evolved counterparts .
Our analysis supports the RGB mass-loss found from asteroseismology and we determine precisely the absolute mass of stars on the lower RGB , M _ { RGB } = 1.15 \pm 0.02 M _ { \sun } .
This will be an important consistency check for the detailed asteroseismology of cluster stars .

Conclusions : Using multiple , detached eclipsing binaries for determining stellar cluster ages , it is now possible to constrain parameters of stellar models , notably the helium content , which were previously out of reach .
By observing a suitable number of detached eclipsing binaries in several open clusters , it will be possible to calibrate the age–scale and the helium enrichment parameter \Delta Y / \Delta Z , and provide firm constraints that stellar models must reproduce .