A fundamental understanding of interfacial processes in nano-confined ionic liquids is crucial to increase the performance of modern energy storage devices. It is well-known that interfaces between electrodes and ionic liquids exhibit structures distinct from that of the bulk liquid. Following the recent interest in these systems, we studied the structure of thin ionic liquid films confined in flexible uncharged carbon nano-pores by using fully-atomistic molecular dynamics simulations. We show that the interfacial ions self-assemble into a closely-packed chequerboard-like pattern, formed by both cations and anions in direct contact with the pore wall, and that within this structure we find changes dependent on the thickness of the confined films. At low coverages a dense layer is formed in which both the imidazolium-ring and its alkyl-tail lie parallel to the pore wall. With increasing coverage the alkyl-chains reorient perpendicular to the surface, making space for additional ions until a densified highly ordered layer is formed. This wall-induced self-patterning into interfacial layers with significantly higher than bulk density is consistent with recent experimental and theoretical studies of similar systems. This work reveals additional molecular-level details on the effect of the film-thickness on the structure and density of the ionic liquid.