By definition, pausing the game will pause character's speech. Are you looking to have the speech continue when paused, or just stay there indefinitely? I'm not sure either would be used enough among other users to warrant a specific setting, but there'll be a workaround.
The former can be done by not pausing the game, but instead using the Engine: Manage systems Action to prevent player interaction and movement while the pause menu is open.
The latter can probably be done by creating another Subtitles Menu that's Appear type is set to Manual, and turning it on as the same time as your Pause menu - effectively swapping out the regular Menu for a "pause-only" one.
You could also just rely on this "Manual" Subtitle Menu entirely - though you'd need to incorporate a custom event to turn it on and off whenever speech starts and stops. A tutorial on custom events, which demonstrates the use of the OnStartSpeech even, can be found here.
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The former can be done by not pausing the game, but instead using the Engine: Manage systems Action to prevent player interaction and movement while the pause menu is open.
The latter can probably be done by creating another Subtitles Menu that's Appear type is set to Manual, and turning it on as the same time as your Pause menu - effectively swapping out the regular Menu for a "pause-only" one.
You could also just rely on this "Manual" Subtitle Menu entirely - though you'd need to incorporate a custom event to turn it on and off whenever speech starts and stops. A tutorial on custom events, which demonstrates the use of the OnStartSpeech even, can be found here.
menu.TurnOff ();
If you comment that out, does that do the trick?