We calculate gauge instanton corrections to a class of higher derivative string effective couplings introduced in . We work in Type I string theory compactified on and realise gauge instantons in terms of D5-branes wrapping the internal space. In the field theory limit we reproduce the deformed ADHM action on a general 惟-background from which one can compute the non-perturbative gauge theory partition function using localisation. This is a non-perturbative extension of and provides further evidence for our proposal of a string theory realisation of the 惟-background.