New measurements and reaction model calculations are reported for single neutron pickup reactions onto a fast uc{22}{Mg} secondary beam at 84 MeV per nucleon. Measurements were made on both carbon and beryllium targets, having very different structures, allowing a first investigation of the likely nature of the pickup reaction mechanism. The measurements involve thick reaction targets and $gamma$-ray spectroscopy of the projectile-like reaction residue for final-state resolution, that permit experiments with low incident beam rates compared to traditional low-energy transfer reactions. From measured longitudinal momentum distributions we show that the $ uc{12}{C} ( uc{22}{Mg}, uc{23}{Mg}+gamma)X$ reaction largely proceeds as a direct two-body reaction, the neutron transfer producing bound uc{11}{C} target residues. The corresponding reaction on the uc{9}{Be} target seems to largely leave the uc{8}{Be} residual nucleus unbound at excitation energies high in the continuum. We discuss the possible use of such fast-beam one-neutron pickup reactions to track single-particle strength in exotic nuclei, and also their expected sensitivity to neutron high-$ell$ (intruder) states which are often direct indicators of shell evolution and the disappearance of magic numbers in the exotic regime.