Halliday & Matthiessen (2014: 515):
A very wide range of different verbs can be pressed into service under this heading, verbs which are not verbs of saying at all but serve in ‘behavioural’ clauses, especially in fictional narrative, to suggest attitudes, emotions or expressive gestures that accompanied the act of speaking, eg sob, snort, twinkle, beam, venture, breathe; e.g.
‘It is a great thing, discretion,’ mused Poirot.
Here the implication is that Poirot is trying to give the impression of thinking aloud, while making sure the listener ‘overhears’.