The Lord be a true and faithful witness... — The emphatic adjuration implies that they are ready to accept the punishment which the righteous Judge will inflict in the event of their proving unfaithful to their promise. The name of the place where they had lately been staying may have reminded them of the history of Genesis 31:49 (though that refers to another Mizpah), in which we find the same formula.
Related Commentaries of Jeremiah 42:5
Jeremiah 42:5-6
5 Then they said to Jeremiah, The LORD be a true and faithful witness between us, if we do not even according to all things for the which the LORD thy God shall send thee to us.
6 Whether it be good, or whether it be evil, we will obey the voice of the LORD our God, to whom we send thee; that it may be well with us, when we obey the voice of the LORD our God.