  We compute the structure factor of the $J_1$-$J_2$ Ising model in an external
field on the square lattice within the Cluster Variation Method. We use a four
point plaquette approximation, which is the minimal one able to capture phases
with broken orientational order in real space, like the recently reported
Ising-nematic phase in the model. The analysis of different local maxima in the
structure factor allows us to track the different phases and phase transitions
against temperature and external field. Although the nematic susceptibility is
not directly related to the structure factor, we show that because of the close
relationship between the nematic order parameter and the structure factor, the
latter shows unambiguous signatures of the presence of a nematic phase, in
agreement with results from direct minimization of a variational free energy.
The disorder variety of the model is identified and the possibility that the
CVM four point approximation be exact on the disorder variety is discussed.
