We present GALEX near-ultraviolet (NUV) and Two-Micron All-Sky Survey J-band photometry for red-sequence galaxies in local clusters. We define quiescent samples according to a strict emission threshold, removing galaxies with very recent star formation. We analyse the NUVJ colour-magnitude relation (CMR) and find that the intrinsic scatter is an order of magnitude larger than for the analogous optical CMR (~0.35 rather than 0.05mag), in agreement with previous studies. Comparing the NUVJ colours with spectroscopically derived stellar population parameters, we find a strong (>5.5sigma) correlation with metallicity, only a marginal trend with age, and no correlation with the alpha/Fe ratio. We explore the origin of the large scatter and conclude that neither aperture effects nor the UV upturn phenomenon contribute significantly. We show that the scatter could be attributed to simple 'frosting' by either a young or a low-metallicity subpopulation.