Tamsin Greig's character doesn't soliloquize, she conspires.
From the independent.co.uk
Portrayed with acidic humor by Linda Kimbrough, Peter's mother doesn't get too much time to soliloquize because her son is such a teller of tall tales.
From the nytimes.com
He'd much rather address the camera and soliloquize on the sorry state of affairs of mankind, though if he says anything memorable, I missed it.
From the washingtonpost.com
This time he advances his narration by bringing his characters onstage alone to soliloquize about what has occurred and what bad results may be expected.
From the time.com
Instead, San Francisco's weary decadence and violence give the Ripper a chance to soliloquize about the nature of evil and a bad man's timeless role in society.
From the denverpost.com
More examples
Monologuize: talk to oneself
A monologue (or monolog) The character may be speaking his or her thoughts aloud, directly addressing another character, or speaking to the audience, especially the former. Monologues are common across the range of dramatic media (plays, films, animation, etc.). ...