drone on
Synonym discussion
Sense: phrasal verb/1
All four phrases describe long, unwelcome speech, but they differ in tone, structure, and register. 'Drone on' specifically highlights a flat, low, monotonous voice — the listener is bored by the tone as much as the length. 'Ramble' focuses on disorganisation: the speaker jumps between unrelated points without a clear direction. 'Hold forth' is more formal and can be neutral or even admiring ('a professor holding forth on ancient philosophy'); the listener may or may not be bored. 'Go on' is the most general and least negative; it can simply mean 'continue speaking at length'. 'Rant' adds anger or strong emotion, whereas 'drone on' is emotionally flat. For everyday use, if you mean someone is putting you to sleep with a flat voice, 'drone on' is the best choice.
Etymology
The verb 'drone' comes from Old English 'drān', meaning a male bee. The low, continuous humming sound of a bee became a metaphor for a person speaking in a flat, monotonous voice. The particle 'on' adds a sense of continuing without stopping, so 'drone on' means to keep talking in that dull way.