I shall not rest __________ I have gone to the bottom of this matter and found the truth.

The sentence expresses that the speaker will not rest up to the point when they have uncovered the truth. 'Until' is the correct conjunction to indicate continuing action up to a specific endpoint or condition. 'After' would reverse the meaning, suggesting rest comes after finding truth. 'While' indicates simultaneity. 'For' indicates duration or reason but does not fit here. Therefore, 'until' is the correct choice.