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Abstract We present the most detailed spectrum of intracluster light (ICL) in an individual cluster to date, the relaxed system RX J2129.7+0005, atz∼ 0.234. Using 15 broadband, deep images observed with the Hubble Space Telescope and JWST in the optical and the infrared, plus deep integral field spectroscopy from MUSE, we computed a total of 3696 ICL maps spanning the spectral range ∼0.4−5μm with our algorithm CICLE, a method that is extremely well suited to analyzing large samples of data in a fully automated way. We used both parametric and nonparametric approaches to fit the spectral energy distribution of the ICL and infer its physical properties, yielding a stellar mass ${\log }_{10}\left(M_{*}/M_{\odot }\right)$between 11.5 and 12.7 and an average age between 9.7 and 10.5 Gyr, from CIGALE and Prospector results. This implies that the ICL in RX J2129.7+0005 is, on average, older than that of disturbed clusters, suggesting that the contribution from different stellar populations to the ICL is at play depending on the cluster’s dynamical state. Coupled with X-ray observations of the hot gas distribution, we confirm the relaxed state of RX J2129.7+0005, showing clear signs of sloshing after a last major merger with a high-mass-ratio satellite that could have happened ∼6.6 Gyr ago in a relatively radial orbit. The presence of substructure in the ICL, such as shells, clouds with different densities and a certain degree of boxyness, and a clump, supports this scenario.