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We present a combined low-temperature time-resolved cathodoluminescence and photoluminescence study of exciton recombination mechanisms in a 3.8 nm thick a-plane (Al,Ga)N/GaN quantum well (QW). We observe the luminescence from QW excitons and from excitons localized on basal stacking faults (BSFs) crossing the QW plane, forming quantum wires (QWRs) at the intersection. We show that the dynamics of QW excitons is dominated by their capture on QWRs, with characteristic decay times ranging from 50 to 350 ps, depending on whether the local density of BSFs is large or small. We therefore relate the multiexponential behavior generally observed by time-resolved photoluminescence in non-polar (Al,Ga)/GaN QW to the spatial dependence of QW exciton dynamics on the local BSF density. QWR exciton decay time is independent of the local density in BSFs and its temperature evolution exhibits a zero-dimensional behavior below 60 K. We propose that QWR exciton localization along the wire axis is induced by well-width fluctuation, reproducing in a one-dimensional system the localization processes usually observed in QWs.