We present GALEX near-UV (NUV) and 2MASS 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 NUV-J 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 0.05 mag), in agreement with previous studies. Comparing the NUV-J 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.