In this work, we describe ab initio calculations and assignment of infrared (IR) spectra of hydrogen-bonded ion-molecular complexes that involve a fluxional proton: the linear N2H+center dot center dot center dot OC and N2D+center dot center dot center dot OC complexes. Given the challenges of describing fluxional proton dynamics and especially its IR activity, we use electric field- driven classical trajectories, i.e., the driven molecular dynamics (DMD) method that was developed by us in recent years and for similar applications, in conjunction with high-level electronic structure theory. Namely, we present a modified and a numerically efficient implementation of DMD specifically for direct (or "on the fly") calculations, which we carry out at the MP2-F12/AVDZ level of theory for the potential energy surface (PES) and MP2/AVDZ for the dipole moment surfaces (DMSs). Detailed analysis of the PES, DMS, and the time-dependence of the first derivative of the DMS, referred to as the driving force, for the highly fluxional vibrations involving H+/D+ revealed that the strongly non-harmonic PES and non-linear DMS yield remarkably complex vibrational spectra. Interestingly, the classical trajectories reveal a doublet in the proton transfer part of the spectrum with the two peaks at 1800 and 1980 cm(-1). We find that their shared intensity is due to a Fermi-like resonance interaction, within the classical limit, of the H+ parallel stretch fundamental and an H+ perpendicular bending overtone. This doublet is also observed in the deuterated species at 1360 and 1460 cm(-1).