A patient with an acute psychotic illness reports seeing vivid colours and hearing music even in a completely silent, dark room, with no real sound or light present to account for either experience. Before revealing the answer: is this synaesthesia?

No, this is more consistent with hallucinations in two modalities than with synaesthesia. Synaesthesia specifically requires a genuine stimulus in one modality to reliably trigger an experience in another; here, there is no real sound or light present at all to account for either the colours or the music, meeting instead the definition of a hallucination arising with no external stimulus that could account for it.