POTENTIAL WICKED EYES AND WICKED HEARTS ENDINGS.
note: an ending being listed here does not indicate my willingness to write it. my blog canon will remain that Celene and Gaspard were blackmailed into a temporary truce, with Celene defeating him between the main game and Trespasser.
Briala's reaction to being shown the locket is neutral. She does not express concern for Celene's safety or reputation for having kept it. Instead, she questions their intentions for bringing it up at all. An example:
What is it you believe you hold, madame Lavellan? A pretty bauble meant to convince me to return to the Empress' shadow?
The point here is that it does not matter that the locket is proof Celene loved her. Briala knows that. It will never overshadow or excuse the fact that Celene had Briala's parents murdered, and that Briala was meant to die with them (Briala doesn't tell the Inquisitor this, though).
I am adjusting Briala's reaction to the Inquisitor prompting Celene for her reward to the following (frankly, she wants to laugh in their faces).
Inquisitor: I think Ambassador Briala deserves some reward for uncovering all this.
Briala: Reward? For returning to the Empress' leash, you mean. No.
Therefore, this route is locked off. Briala will simply exit the conversation, and if she doesn't have her mother's locket back in her possession, she soon will.
With evidence of his attempted coup in Celene's hands, Gaspard is executed. Briala and her agents will disappear from the palace during resulting cutscenes (assisted by Felassan if necessary) and appear to vanish.
Gaspard may not be the player of the Game Celene was, but he is no fool; he recognizes the threat Briala poses. His efforts to capture her, should she escape this night, will be extensive.
This will not last. Gaspard will not suffer being a puppet; Briala does not survive this.
As this is not an ending I'm interested in exploring, this is as far as my analysis goes.
Public truce (in-game version).
Briala will abide by this, for a time. She is not, however, constrained by the same codes and rules that the others' power and influence holds them to. The "blackmail" leveraged against her is, frankly, laughable.
If Celene prevails in the end, Briala's rebellion succeeds. If Gaspard defeats Celene, however, Briala likely fails.