The Barely Off-Shell Nucleon Structure (BONuS) experiment at CLAS12, at Jefferson Lab, will measure the neutron structure function $F_2$ for $0.1 < x < 0.8$ over a broad $Q^2$ range, from 1 to 14 GeV$^2 /c$, using electron scattering from deuterium with spectator-proton tagging. By selecting the low-momentum recoil protons at large backward angles, final-state interactions as the deuteron breaks up can be minimized, and the deep-inelastic kinematics for the neutron can be determined. This technique, which has been used successfully at CLAS at 6 GeV, will be extended to a beam energy of 11 GeV with significantly increased luminosity. Details of the BONuS third generation Radial Time Projection Chamber and expected high-$x$ $F_2 ^n$ results are presented.